{"title":"Stochastics Books","description":"","products":[{"product_id":"probability-9780198709978","title":"Probability","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProbability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters'' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.A special feature is the authors'' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART A BASIC PROBABILITY; PART B FURTHER PROBABILITY","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732767650135,"sku":"9780198709978","price":38.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198709978.jpg?v=1719998311"},{"product_id":"probability-and-random-processes-9780198847595","title":"Probability and Random Processes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe fourth edition of this successful text provides an introduction to probability and random processes, with many practical applications. It is aimed at mathematics undergraduates and postgraduates, and has four main aims.US BL To provide a thorough but straightforward account of basic probability theory, giving the reader a natural feel for the subject unburdened by oppressive technicalities. BE BL To discuss important random processes in depth with many examples.BE BL To cover a range of topics that are significant and interesting but less routine. BE BL To impart to the beginner some flavour of advanced work.BE UE OP The book begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic calculus with Itô''s formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, Lévy processes, self-similarity and stability, time changes, and the holding-time\/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1300, and many of the existing exercises have been refreshed by additional parts. The solutions to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition, (OUP 2020).CP\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eFeatures of PRP include brief but helpful motivational introductions to each subsection, and copious references to historical applications. To aid navigation, definitions, theorems and other key results are highlighted, using three different colours. The tone throughout is rigorous but the touch is human ... * Owen Toller, The Mathematical Gazette *\u003cbr\u003eSince its first appearance in 1982 Probability and Random Processes has been a landmark book on the subject and has become mandatory reading for any mathematician wishing to understand chance. It is aimed mainly at final-year honours students and graduate students, but it goes beyond this level, and all serious mathematicians and academic libraries should own a copy ... the companion book of exercises is cleverly conceived and ... forms a perfect complement to the main text. * Times Higher Education Supplement *\u003cbr\u003eReview from previous edition...a full and comprehensive account of (almost all) the probability theory and stochastic processes one could hope to teach to undergraduates.... As well as its masterful coverage of the material, the book has many appealing stylistic features ... extremely valuable in finding good proofs of theorems which are dealt with rather cursorily in other textbooks. * The Mathematical Gazette  *\u003cbr\u003eOne of the strong features of the book is its large collection of interesting exercises, which has been greatly expanded in this new edition so that there are now over one thousand. These are conveniently collected together in a separate volume that includes full solutions. * Biometrics *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Events and their probabilities 2: Random variables and their distributions 3: Discrete random variables 4: Continuous random variables 5: Generating functions and their applications 6: Markov chains 7: Convergence of random variables 8: Random processes 9: Stationary processes 10: Renewals 11: Queues 12: Martingales 13: Diffusion processes","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732810641751,"sku":"9780198847595","price":50.35,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198847595.jpg?v=1719998497"},{"product_id":"all-of-statistics-9781441923226","title":"All of Statistics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTaken literally, the title All of Statistics is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics.                            This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book                            includes modern topics like nonparametric curve estimation, bootstrapping, and clas sification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No                            previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analyzing data. For some time, statistics research was con ducted in statistics                            departme\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eWinner of the 2005 DeGroot Prize.\u003c\/p\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e\"Presuming no previous background in statistics and described by the author as \"demanding\" yet \"understandable because the material is as intuitive as possible\" (p. viii), this certainly would be my choice of textbook if I was required to learn mathematical statistics again for a couple of semesters.\" \u003ci\u003eTechnometrics, August 2004\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\"This book should be seriously considered as a text for a theoretical statsitics course for non-majors, and perhaps even for majors...The coverage of emerging and important topics is timely and welcomed...you should have this book on your desk as a reference to nothing less than 'All of Statistics.'\" \u003ci\u003eBiometrics, December 2004\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\"Although \u003ci\u003eAll of Statistics\u003c\/i\u003e is an ambitious title, this book is a concise guide, as the subtitle suggests....I recommend it to anyone who has an interest in learning something new about statistical inference. There is something here for everyone.\" \u003ci\u003eThe American Statistician, May 2005\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\"As the title of the book suggests, ‘All of Statistics’ covers a wide range of statistical topics. … The number of topics covered in this book is vast … . The greatest strength of this book is as a first point of reference for a wide range of statistical methods. … I would recommend this book as a useful and interesting introduction to a large number of statistical topics for non-statisticians and also as a useful reference book for practicing statisticians.\" (Matthew J. Langdon, Journal of Applied Statistics, Vol. 32 (1), January, 2005)\u003c\/p\u003e\u003cp\u003e\"This book was written specifically to give students a quick but sound understanding of modern statistics, and its coverage is very wide. … The book is extremely well done … .\" (N. R. Draper, Short Book Reviews, Vol. 24 (2), 2004)\u003c\/p\u003e\u003cp\u003e\"This is most definitely a book about mathematical statistics. It is full of theorems and proofs … . Presuming no previous background in statistics … this certainly would be my choice of textbook if I was required to learn mathematical statistics again for a couple of semesters.\" (Eric R. Ziegel, Technometrics, Vol. 46 (3), August, 2004)\u003c\/p\u003e\u003cp\u003e\"The author points out that this book is for those who wish to learn probability and statistics quickly … . this book will serve as a guideline for instructors as to what should constitute a basic education in modern statistics. It introduces many modern topics … . Adequate references are provided at the end of each chapter which the instructor will be able to use profitably … .\" (Arup Bose, Sankhya, Vol. 66 (3), 2004)\u003c\/p\u003e\u003cp\u003e\"The amount of material that is covered in this book is impressive. … the explanations are generally clear and the wide range of techniques that are discussed makes it possible to include a diverse set of examples … . The worked examples are complemented with numerous theoretical and practical exercises … . is a very useful overview of many areas of modern statistics and as such will be very useful to readers who require such a survey. Library copies would also see plenty of use.\" (Stuart Barber, Journal of the Royal Statistical Society, Series A – Statistics in Society, Vol. 168 (1), 2005)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eProbability.- Random Variables.- Expectation.- Inequalities.- Convergence of Random Variables.- Models, Statistical Inference and Learning.- Estimating the CDF and Statistical Functionals.- The Bootstrap.- Parametric Inference.- Hypothesis Testing and p-values.- Bayesian Inference.- Statistical Decision Theory.- Linear and Logistic Regression.- Multivariate Models.- Inference about Independence.- Causal Inference.- Directed Graphs and Conditional Independence.- Undirected Graphs.- Loglinear Models.- Nonparametric Curve Estimation.- Smoothing Using Orthogonal Functions.- Classification.- Probability Redux: Stochastic Processes.- Simulation Methods.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739209740631,"sku":"9781441923226","price":49.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441923226.jpg?v=1720051498"},{"product_id":"a-modern-introduction-to-probability-and-statistics-understanding-why-and-how-9781849969529","title":"A Modern Introduction to Probability and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSuitable for self study  \u003cp\u003eUse real examples and real data sets that will be familiar to the audience  \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003eIntroduction to the bootstrap is included – this is a modern method missing in many other books  \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"[the material is] superbly motivated with interest-grabbing examples... exercises excellent and plentiful.\" Edward Williams, University of Michigan-Dearborn, USA\u003c\/p\u003e \u003cp\u003e\"... it is a notoriously hard task to introduce probability and statistics with a mix of intuition and mathematics to keep students motivated. Therefore, I very much welcome this book and recommend it as course material.\" Sara van de Geer, Leiden University, The Netherlands \u003c\/p\u003e \u003cp\u003e\"This textbook provides a well-written first course in probability and statistics...It is a book that has been written based on the long teaching experience of the authors and I would certainly recommend it for university coursework.\" \u003cem\u003eShort Book Reviews of the International Statistical Institute,  December 2005\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"This book has numerous quick exercises to give direct feedback to the students. … A website at www.springeronline.com\/978-1-85233-896-1 gives access to the data files used in the text … . This will be a key text for undergraduates in computer science, physics, mathematics, chemistry, biology and business studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.\" (Rainer Beedgen, Zentralblatt MATH, Vol. 1079, 2006)\u003c\/p\u003e \u003cp\u003e\"The book is designed for a one-semester introductory course in probability and statistics basics for engineering students. … It can also be used by students in other more mathematically oriented majors such as applied mathematics with more emphasis on the mathematics and additional coverage in topics such as combinatorics, conditional expectation, and generating functions. … More elaborate exercises and real datasets are given at the end of each chapter.\" (Arthur B. Yeh, Technometrics, Vol. 49 (3), August, 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eWhy probability and statistics?.- Outcomes, events, and probability.- Conditional probability and independence.- Discrete random variables.- Continuous random variables.- Simulation.- Expectation and variance.- Computations with random variables.- Joint distributions and independence.- Covariance and correlation.- More computations with more random variables.- The Poisson process.- The law of large numbers.- The central limit theorem.- Exploratory data analysis: graphical summaries.- Exploratory data analysis: numerical summaries.- Basic statistical models.- The bootstrap.- Unbiased estimators.- Efficiency and mean squared error.- Maximum likelihood.- The method of least squares.- Confidence intervals for the mean.- More on confidence intervals.- Testing hypotheses: essentials.- Testing hypotheses: elaboration.- The t-test.- Comparing two samples.","brand":"Springer London Ltd","offers":[{"title":"Default Title","offer_id":48742309527895,"sku":"9781849969529","price":29.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781849969529.jpg?v=1720060873"},{"product_id":"numerical-methods-for-solving-discrete-event-systems-with-applications-to-queueing-systems-9783031100819","title":"Numerical Methods for Solving Discrete Event","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis graduate textbook provides an alternative to discrete event simulation.  It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.\u003c\/p\u003eThe material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This monograph is an exciting addition to the queueing\/stochastic processes literature,\u003cbr\u003e written by two highly respected senior researchers. … The writing is precise and clear. Well-known models are used as examples to illustrate the methods presented. … It has a huge number of powerful techniques that are not given sufficient focus elsewhere. This may be one of the best books to introduce graduate students … . This monograph is essential for the bookshelf … of every serious queueing theorist.” (Myron Hlynka, Mathematical Reviews, December, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasic Concepts and Definitions.- Systems with Events Generated by Poisson or by Binomial Processes.- Generating the Transition Matrix.- Systems with Events Created by Renewal Processes.- Systems with Events Created by Phase-type Processes.- Computational Complexity and Rounding and Truncation Errors.- Transient Solutions of Markov Chains.- Moving Toward the Statistical Equilibrium.- Equilibrium Solutions of Markov Chains and Related Topics.- Reducing the State Space Through Censoring and Embedding.- Systems with Independent or Almost Independent Components.- Infinite-State Markov Chains and Matrix Analytic Methods.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743069516119,"sku":"9783031100819","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031100819.jpg?v=1720063974"},{"product_id":"measure-theory-probability-and-stochastic-processes-9783031142048","title":"Measure Theory, Probability, and Stochastic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.\u003c\/p\u003eArranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eMeasure Theory, Probability, and Stochastic Processes\u003c\/i\u003e is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author’s more advanced textbook in the same series (GTM 274).\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I. Measure Theory.- Chapter 1. Measurable Spaces.- Chapter 2. Integration of Measurable Functions.- Chapter 3. Construction of Measures.- Chapter 4. Lp Spaces.- Chapter 5. Product Measure.- Chapter 6. Signed Measures.- Chapter 7. Change of Variables.- Part II. Probability Theory.- Chapter 8. Foundations of Probability Theory.- Chapter 9. Independence.- Chapter 10. Convergence of Random Variables.- Chapter 11. Conditioning.- Part III. Stochastic Processes.- Chapter 12. Theory of Martingales.- Chapter 13. Markov Chains.- Chapter 14. Brownian Motion.  ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743072629079,"sku":"9783031142048","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"an-introduction-to-optimal-control-theory-the-dynamic-programming-approach-9783031211386","title":"An Introduction to Optimal Control Theory: The","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others.\u003c\/p\u003e  The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations.\u003c\/p\u003e  \u003cp\u003eThe first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction: optimal control problems-. Discrete-time deterministic systems.- Discrete-time stochastic control systems.- Continuous-time deterministic systems.- Continuous-time Markov control processes.- Controlled diffusion processes.- Appendices.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743075840343,"sku":"9783031211386","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031211386.jpg?v=1720064003"},{"product_id":"brownian-motion-martingales-and-stochastic-calculus-9783319310886","title":"Brownian Motion, Martingales, and Stochastic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.\u003cbr\u003eSince its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. \u003ci\u003eBrownian Motion, Martingales, and Stochastic Calculus\u003c\/i\u003e provides a strong theoretical background to the reader interested in such developments.\u003cbr\u003eBeginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“‘The aim of this book is to provide a rigorous introduction to the theory of stochastic calculus for continuous semi-martingales putting a special emphasis on Brownian motion.’ … If the reader has the background and needs a rigorous treatment of the subject this book would be a good choice. Le Gall writes clearly and gets to the point quickly … .” (Richard Durrett, MAA Reviews, March, 2017) \u003cp\u003e\u003c\/p\u003e\u003cp\u003e“The purpose of this book is to provide concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. … The book is written very clearly, it is interesting both for its construction and maintenance, mostly it is self-contained. It can be recommended to everybody who wants to study stochastic calculus, including those who is interested to its applications in other fields.” (Yuliya S. Mishura, zbMATH, 2017)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGaussian variables and Gaussian processes.- Brownian motion.- Filtrations and martingales.- Continuous semimartingales.- Stochastic integration.- General theory of Markov processes.- Brownian motion and partial differential equations.- Stochastic differential equations.- Local times.- The monotone class lemma.- Discrete martingales.- References.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743094124887,"sku":"9783319310886","price":38.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319310886.jpg?v=1720064084"},{"product_id":"probability-essentials-9783540438717","title":"Probability Essentials","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"(The book is) a lean and largely self-contained introduction to the modern theory of probability, aimed at advanced undergraduate or beginning graduate students. The 28 short chapters belie the book's genesis as polished lecture notes; the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises. ... The authors make it clear what luggage is required for this exhilarating trek,... a good knowledge of advanced calculus, some linear algebra, and some \"mathematical sophistication\". With this understood, the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery. Within the constraints of a slim volume, it is hard to imagine how the authors could have done a more effective or more attractive job.\" The Mathematical Gazette, Vol. 84, No 500, 2000 \"The authors provide the shortest path through the twenty-eight chapter headings. The topics are treated in a mathematically and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. ... Numerous exercises add to the value of the text as a teaching tool. In conclusion, this is an excellent text for the intended audience.\"\u003cbr\u003eShort Book Reviews, Vol. 21, No. 2, 2001\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure 10. Independent Random Variables 11. Probability Distributions on R 12. Probability Distributions on Rn 13. Characteristic Functions 14. Properties of Characteristic Functions 15. Sums of Independent Random Variables 16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) 17. Convergence of Random Variables 18. Weak Convergence 19. Weak Convergence and Characteristic Functions 20. The Laws of Large Numbers 21. The Central Limit Theorem 22. L2 and Hilbert Spaces 23. Conditional Expectation 24. Martingales 25. Supermartingales and Submartingales 26. Martingale Inequalities 27. Martingales Convergence Theorems 28. The Radon-Nikodym Theorem","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743130759511,"sku":"9783540438717","price":52.24,"currency_code":"GBP","in_stock":true}]},{"product_id":"stochastic-processes-and-financial-mathematics-9783662647103","title":"Stochastic Processes and Financial Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while at the same time placing much emphasis on good readability, motivation, and explanation of the issues covered. \u003cbr\u003eFinancial mathematical topics are first introduced in the context of discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central results of stochastic analysis such as the Itô formula, Girsanov's theorem and martingale representation theorems are of fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of topics.\u003cbr\u003e\u003cbr\u003eAdvanced knowledge of probability theory is assumed, in particular of discrete-time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, Lévy processes, processes with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading and for instructors as a basis for their own courses.\u003cp\u003eThis book is a translation of the original German 1st \u003ci\u003eedition Stochastische Prozesse und Finanzmathematik\u003c\/i\u003e by Ludger Rüschendorf, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eOption pricing in models in discrete time.- Scorohod's embedding theorem and Donsker's theorem.- Stochastic integration.- Elements of stochastic analysis.- Option pricing in complete and incomplete markets.- Utility optimization, minimum distance martingales, and utility indiff.- Variance-minimum hedging.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743142949207,"sku":"9783662647103","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662647103.jpg?v=1720064297"},{"product_id":"introduction-to-stochastic-calculus-9789811083175","title":"Introduction to Stochastic Calculus","description":"This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.\u003cbr\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743275102551,"sku":"9789811083174","price":85.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811083174.jpg?v=1720064877"},{"product_id":"understanding-markov-chains-examples-and-applications-9789811306587","title":"Understanding Markov Chains: Examples and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eProbability Background.-  Gambling Problems.- Random Walks.- Discrete-Time Markov Chains.- First Step Analysis.- Classification of States.- Long-Run Behavior of Markov Chains.- Branching Processes.- Continuous-Time Markov Chains.- Discrete-Time Martingales.- Spatial Poisson Processes.- Reliability Theory.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743286767959,"sku":"9789811306587","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811306587.jpg?v=1720064930"},{"product_id":"information-theory-and-network-coding-information-technology-transmission-processing-and-storage-9780387792330","title":"Information Theory and Network Coding Information","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"This book could serve as a reference in the general area of information theory and would be of interest to electrical engineers, computer engineers, or computer scientists with an interest in information theory. Each chapter has an appropriate problem set at the end and a brief paragraph that provides insight into the historical significance of the material covered therein. … Summing Up: Recommended. Upper-division undergraduate through professional collections.\" (J. Beidler, Choice, Vol. 46 (9), May, 2009)\u003c\/p\u003e \u003cp\u003e\"The book consisting of 21 chapters is divided into two parts. Part I, Components of Information Theory … . Part II Fundamentals of Network Coding … . A comprehensive instructor’s manual is available. This is a well planned comprehensive book on the subject. The writing style of the author is quite reader friendly. … it is a welcome addition to the subject and will be very useful to students as well as to the researchers in the field.\" (Arjun K. Gupta, Zentralblatt MATH, Vol. 1154, 2009)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Science of Information.- The Science of Information.- Fundamentals of Network Coding.- Information Measures.- Information Measures.- Zero-Error Data Compression.- Weak Typicality.- Strong Typicality.- Discrete Memoryless Channels.- Rate-Distortion Theory.- The Blahut–Arimoto Algorithms.- Differential Entropy.- Continuous-Valued Channels.- Markov Structures.- Information Inequalities.- Shannon-Type Inequalities.- Beyond Shannon-Type Inequalities.- Entropy and Groups.- Fundamentals of Network Coding.- The Max-Flow Bound.- Single-Source Linear Network Coding: Acyclic Networks.- Single-Source Linear Network Coding: Cyclic Networks.- Multi-source Network Coding.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48864540262743,"sku":"9780387792330","price":71.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387792330.jpg?v=1722272386"},{"product_id":"stochastic-thermodynamics-9780691201771","title":"Stochastic Thermodynamics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865545388375,"sku":"9780691201771","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"estimation-of-stochastic-processes-with-missing-observations-9781536158908","title":"Estimation of Stochastic Processes with Missing","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWe propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing. Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886135554391,"sku":"9781536158908","price":163.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781536158908.jpg?v=1722538943"},{"product_id":"cooperative-effects-in-stochastic-models-9781594542527","title":"Cooperative Effects in Stochastic Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe monograph is devoted to an investigation of co-operative effects in stochastic models. It includes original results of the authors in the last decade. The main object of the monograph is an analysis of an influence of a stochastic model structure on its characteristics. Problems of a co-operation and a decomposition are actual in a solution of a lot of concrete problems. These problems are: a parallelisation of algorithms and programs, a modelling of supercomputers, computer networks, systems of mobile telephones catastrophes in complex systems, a design and an improvement of technological and economical processes etc. The co-operative effects create a source of significant dependencies between complex system characteristics under large random disturbances. To analyse these effects is necessary to create special methods based on structural analysis of multi-element stochastic models together with majoral asymptotic bounds of these models characteristics. At the same time it demands to develop new approaches to a processing of statistical data and a skill in an usage of the probability theory limit theorems and related asymptotic series and bounds. A choice of the monograph material is defined as by initial applied problems so by probability methods of their solution. Conditionally the monograph may be divided into two parts. First of them contains four sections devoted to a finding of the co-operative effects and to a development of new related analytical and numerical methods. This part has presumably methodological character and creates a theoretical base of an investigation of applied stochastic systems. Second part contains three sections devoted to a solution of different applied problems. It has some interesting substantial results.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886515466583,"sku":"9781594542527","price":155.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781594542527.jpg?v=1722540404"},{"product_id":"distributions-in-stochastic-network-models-9781604561432","title":"Distributions in Stochastic Network Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886629138775,"sku":"9781604561432","price":99.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781604561432.jpg?v=1722540948"},{"product_id":"simulation-9780323857390","title":"Simulation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This textbook contains and describes all the tools one needs to plan and to carry out a simulation study as well as to analyze its results.\" --J.Wolters, zbMATH Open  \"It presents the statistics needed to analyze simulated data and to validate the simulation model. In this edition, several new topics are included as well as a number of new exercises.\" --Vigirdas Mackevicius, zbMATH Open\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction 2. Elements of Probability 3. Random Numbers 4. Generating Discrete Random Variables 5. Generating Continuous Random Variables 6. The Multivariate Normal Distribution and Copulas 7. The Discrete Event Simulation Approach 8. Statistical Analysis of Simulated Data 9. Variance Reduction Techniques 10. Additional Variance Reduction Techniques 11. Statistical Validation Techniques 12. Markov Chain Monte Carlo Methods","brand":"Elsevier Science \u0026 Technology","offers":[{"title":"Default Title","offer_id":49083476640087,"sku":"9780323857390","price":69.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780323857390.jpg?v=1725549069"},{"product_id":"stochastic-processes-9781906574307","title":"Stochastic Processes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"New Academic Science Ltd","offers":[{"title":"Default Title","offer_id":49084602417495,"sku":"9781906574307","price":47.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781906574307.jpg?v=1725552728"},{"product_id":"probability-an-introduction-through-theory-and-exercises-9783031384912","title":"Probability: An Introduction Through Theory and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.\u003c\/p\u003e  \u003cp\u003eThe book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.\u003c\/p\u003e  \u003cp\u003eBased on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084758884695,"sku":"9783031384912","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031384912.jpg?v=1725553247"},{"product_id":"design-and-analysis-of-experiments-9783319522487","title":"Design and Analysis of Experiments","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book offers a step-by-step guide to the experimental planning process and the ensuing analysis of normally distributed data, emphasizing the practical considerations governing the design of an experiment. Data sets are taken from real experiments and sample SAS programs are included with each chapter. Experimental design is an essential part of investigation and discovery in science; this book will serve as a modern and comprehensive reference to the subject.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“The textbook provides a practically oriented version of design and analysis of experiments. The corresponding methods are illustrated by means of numerous simple experiments. Thus, the models and methods are equipped with many examples, exercises, numerical results and related tables and figures. ... The present volume can be recommended as textbook for lectures on models and methods of experimental design as well as handbook for use in practice.” (Kurt Marti, zbMATH 1383.62001, 2018)\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePrinciples and Techniques.- Planning Experiments.- Designs With One Source of Variation.- Inferences for Contrasts and Treatment Means.- Checking Model Assumptions.- Experiments With Two Crossed Treatment Factors.- Several Crossed Treatment Factors.- Polynomial Regression.- Analysis of Covariance.- Complete Block Designs.- Incomplete Block Designs.- Designs With Two Blocking Factors.- Confounded Two-Level Factorial Experiments.- Confounding in General Factorial Experiments.- Fractional Factorial Experiments.- Response Surface Methodology.- Random Effects and Variance Components.- Nested Models.- Split-Plot Designs\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084768878935,"sku":"9783319522487","price":104.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319522487.jpg?v=1725553281"},{"product_id":"markov-chains-9783319977034","title":"Markov Chains","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. \u003c\/p\u003e  \u003cp\u003ePart I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). \u003c\/p\u003e  \u003cp\u003ePart III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I Foundations.- Markov Chains: Basic Definitions.- Examples of Markov Chains.- Stopping Times and the Strong Markov Property.- Martingales, Harmonic Functions and Polsson-Dirichlet  Problems.- Ergodic Theory for Markov Chains.- Part II Irreducible Chains: Basics.- Atomic Chains.- Markov Chains on a Discrete State Space.- Convergence of Atomic Markov Chains.- Small Sets, Irreducibility and Aperiodicity.- Transience, Recurrence and Harris Recurrence.- Splitting Construction and Invariant Measures.- Feller and T-kernels.- Part III Irreducible Chains: Advanced Topics.- Rates of Convergence for Atomic Markov Chains.- Geometric Recurrence and Regularity.- Geometric Rates of Convergence.- (\u003ci\u003ef, r\u003c\/i\u003e)-recurrence and Regularity.- Subgeometric Rates of Convergence.- Uniform and \u003ci\u003eV\u003c\/i\u003e-geometric Ergodicity by Operator Methods.- Coupling for Irreducible Kernels.- Part IV Selected Topics.- Convergence in the Wasserstein Distance.- Central Limit Theorems.- Spectral Theory.- Concentration Inequalities.- Appendices.- A Notations.- B Topology, Measure, and Probability.- C Weak Convergence.- D Total and V-total Variation Distances.- E Martingales.- F Mixing Coefficients.- G Solutions to Selected Exercises.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084770550103,"sku":"9783319977034","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319977034.jpg?v=1725553285"},{"product_id":"basic-stochastic-processes-a-course-through-exercises-9783540761754","title":"Basic Stochastic Processes: A Course Through","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eStochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book fulfils its aim of providing good and interesting material for advanced undergraduate study.\u003c\/p\u003e \u003cp\u003eThe Times Higher Education Supplement\u003c\/p\u003e \u003cp\u003eThis is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systems\u003c\/p\u003e \u003cp\u003ewww.quantnotes.com\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Review of Probability.- 1.1 Events and Probability.- 1.2 Random Variables.- 1.3 Conditional Probability and Independence.- 1.4 Solutions.- 2. Conditional Expectation.- 2.1 Conditioning on an Event.- 2.2 Conditioning on a Discrete Random Variable.- 2.3 Conditioning on an Arbitrary Random Variable.- 2.4 Conditioning on a ?-Field.- 2.5 General Properties.- 2.6 Various Exercises on Conditional Expectation.- 2.7 Solutions.- 3. Martingales in Discrete.- 3.1 Sequences of Random Variables.- 3.2 Filtrations.- 3.3 Martingales.- 3.4 Games of Chance.- 3.5 Stopping Times.- 3.6 Optional Stopping Theorem.- 3.7 Solutions.- 4. Martingale Inequalities and Convergence.- 4.1 Doob’s Martingale Inequalities.- 4.2 Doob’s Martingale Convergence Theorem.- 4.3 Uniform Integrability and L1 Convergence of Martingales.- 4.4 Solutions.- 5. Markov Chains.- 5.1 First Examples and Definitions.- 5.2 Classification of States.- 5.3 Long-Time Behaviour of Markov Chains: General Case.- 5.4 Long-Time Behaviour of Markov Chains with Finite State Space.- 5.5 Solutions.- 6. Stochastic Processes in Continuous Time.- 6.1 General Notions.- 6.2 Poisson Process.- 6.2.1 Exponential Distribution and Lack of Memory.- 6.2.2 Construction of the Poisson Process.- 6.2.3 Poisson Process Starts from Scratch at Time t.- 6.2.4 Various Exercises on the Poisson Process.- 6.3 Brownian Motion.- 6.3.1 Definition and Basic Properties.- 6.3.2 Increments of Brownian Motion.- 6.3.3 Sample Paths.- 6.3.4 Doob’s Maximal L2 Inequality for Brownian Motion.- 6.3.5 Various Exercises on Brownian Motion.- 6.4 Solutions.- 7. Itô Stochastic Calculus.- 7.1 Itô Stochastic Integral: Definition.- 7.2 Examples.- 7.3 Properties of the Stochastic Integral.- 7.4 Stochastic Differential and Itô Formula.- 7.5 Stochastic Differential Equations.- 7.6 Solutions.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49084775268695,"sku":"9783540761754","price":28.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540761754.jpg?v=1725553300"},{"product_id":"stochastic-differential-equations-an-introduction-with-applications-9783540047582","title":"Stochastic Differential Equations: An","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new exercises (without solutions) have beed added. They have all been placed in the end of each chapter, in order to facilitate the use of this edition together with previous ones. Several errors have been corrected and formulations have been improved. This has been made possible by the valuable comments from (in alphabetical order) Jon Bohlin, Mark Davis, Helge Holden, Patrick Jaillet, Chen Jing, Natalia Koroleva,MarioLefebvre,Alexander Matasov,Thilo Meyer-Brandis, Keigo Osawa, Bjorn Thunestvedt, Jan Uboe and Yngve Williassen. I thank them all for helping to improve the book. My thanks also go to Dina Haraldsson, who once again has performed the typing and drawn the ?gures with great skill. Blindern, September 2002 Bernt Oksendal xv Preface to Corrected Printing, Fifth Edition The main corrections and improvements in this corrected printing are from Chapter 12. I have bene?tted from useful comments from a number of p- ple, including (in alphabetical order) Fredrik Dahl, Simone Deparis, Ulrich Haussmann, Yaozhong Hu, Marianne Huebner, Carl Peter Kirkebo, Ni- lay Kolev, Takashi Kumagai, Shlomo Levental, Geir Magnussen, Anders Oksendal, Jur . . gen Pottho?, Colin Rowat, Stig Sandnes, Lones Smith, S- suo Taniguchi and Bjorn Thunestvedt. I want to thank them all for helping me making the book better. I also want to thank Dina Haraldsson for pro?cient typing.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the fifth edition:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"This is a highly readable and refreshingly rigorous introduction to stochastic calculus. … This is not a watered-down treatment. It is a serious introduction that starts with fundamental measure-theoretic concepts and ends, coincidentally, with the Black-Scholes formula as one of several examples of applications. This is the best single resource for learning the stochastic calculus … .\" (riskbook.com, 2002)\u003c\/p\u003e \u003cp\u003eFrom the reviews of the sixth edition:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"The book … has evolved from a 200-page typewritten booklet to a modern classic. Part of its charm and success is the fact that the author does not bother too much with the (for the novice) cumbersome rigorous theory … . This does not mean that the book is not rigorous, it is just the timing and dosage of mathematical rigour … that is palatable for undergraduates … . a highly readable account, suitable for self-study and for use in the classroom.\" (René L. Schilling, The Mathematical Gazette, March, 2005)\u003c\/p\u003e \u003cp\u003e\"This is the sixth edition of the classical and excellent book on stochastic differential equations. The main difference with the next to last edition is the addition of detailed solutions of selected exercises … . This is certainly an excellent idea in view to test its ability of applications of the concepts … . certainly one of the best books on the subject, it will be very helpful to any graduate students and also very valuable for any analysts of financial market.\" (Stéphane Métens, Physicalia, Vol. 26 (1), 2004)\u003c\/p\u003e \u003cp\u003e\"This is now the sixth edition of the excellent book on stochastic differential equations and related topics. … the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study.\" (Evelyn Buckwar, Zentralblatt MATH, Vol. 1025, 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eSome Mathematical Preliminaries.- Itô Integrals.- The Itô Formula and the Martingale Representation Theorem.- Stochastic Differential Equations.- The Filtering Problem.- Diffusions: Basic Properties.- Other Topics in Diffusion Theory.- Applications to Boundary Value Problems.- Application to Optimal Stopping.- Application to Stochastic Control.- Application to Mathematical Finance.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49084775530839,"sku":"9783540047582","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540047582.jpg?v=1725553299"},{"product_id":"informal-introduction-to-stochastic-calculus-with-applications-an-9789811247569","title":"Informal Introduction To Stochastic Calculus With","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMost branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop.  Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.This edition has also improved presentation from the first edition in several chapters, including new material.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":49084929638743,"sku":"9789811247569","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811247569.jpg?v=1725553779"},{"product_id":"a-first-course-in-bayesian-statistical-methods-9780387922997","title":"A First Course in Bayesian Statistical Methods","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003col\u003e\n\u003cli\u003e\u003cp\u003eA self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. \u003c\/p\u003e\u003c\/li\u003e\n\u003cli\u003e\u003cp\u003eThe development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.\u003c\/p\u003e\u003c\/li\u003e\n\u003c\/ol\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003eThis is an excellent book for its intended audience: statisticians who wish to learn Bayesian methods. Although designed for a statistics audience, it would also be a good book for econometricians who have been trained in frequentist methods, but wish to learn Bayes. In relatively few pages, it takes the reader through a vast amount of material, beginning with deep issues in statistical methodology such as de Finetti’s theorem, through the nitty-gritty of Bayesian computation to sophisticated models such as generalized linear mixed effects models and copulas. And it does so in a simple manner, always drawing parallels and contrasts between Bayesian and frequentist methods, so as to allow the reader to see the similarities and differences with clarity. (Econometrics Journal) “Generally, I think this is an excellent choice for a text for a one-semester Bayesian Course. It provides a good overview of the basic tenets of Bayesian thinking for the common one and two parameter distributions and gives introductions to Bayesian regression, multivariate-response modeling, hierarchical modeling, and mixed effects models. The book includes an ample collection of exercises for all the chapters. A strength of the book is its good discussion of Gibbs sampling and Metropolis-Hastings algorithms. The author goes beyond a description of the MCMC algorithms, but also provides insight into why the algorithms work. …I believe this text would be an excellent choice for my Bayesian class since it seems to cover a good number of introductory topics and giv the student a good introduction to the modern computational tools for Bayesian inference with illustrations using R. (Journal of the American Statistical Association, June 2010, Vol. 105, No. 490)\u003c\/p\u003e\u003cp\u003e“Statisticians and applied scientists. The book is accessible to readers having a basic familiarity with probability theory and grounding statistical methods. The author has succeeded in writing an acceptable introduction to the theory and application of Bayesian statistical methods which is modern and covers both the theory and practice. … this book can be useful as a quick introduction to Bayesian methods for self study. In addition, I highly recommend this book as a text for a course for Bayesian statistics.” (Lasse Koskinen, International Statistical Review, Vol. 78 (1), 2010)\u003c\/p\u003e\u003cp\u003e“The book under review covers a balanced choice of topics … presented with a focus on the interplay between Bayesian thinking and the underlying mathematical concepts. … the book by Peter D. Hoff appears to be an excellent choice for a main reading in an introductory course. After studying this text the student can go in a direction of his liking at the graduate level.” (Krzysztof Łatuszyński, Mathematical Reviews, Issue 2011 m)\u003c\/p\u003e\u003cp\u003e“The book is a good introductory treatment of methods of Bayes analysis. It should especially appeal to the reader who has had some statistical courses in estimation and modeling, and wants to understand the Bayesian interpretation of those methods. Also, readers who are primarily interested in modeling data and who are working in areas outside of statistics should find this to be a good reference book. … should appeal to the reader who wants to keep with modern approaches to data analysis.” (Richard P. Heydorn, Technometrics, Vol. 54 (1), February, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eand examples.- Belief, probability and exchangeability.- One-parameter models.- Monte Carlo approximation.- The normal model.- Posterior approximation with the Gibbs sampler.- The multivariate normal model.- Group comparisons and hierarchical modeling.- Linear regression.- Nonconjugate priors and Metropolis-Hastings algorithms.- Linear and generalized linear mixed effects models.- Latent variable methods for ordinal data.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49371711209815,"sku":"9780387922997","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387922997.jpg?v=1730154260"},{"product_id":"introduction-to-probability-and-statistics-for-engineers-and-scientists-9780128243466","title":"Introduction to Probability and Statistics for","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCHAPTER 1 Introduction to statistics   CHAPTER 2 Descriptive statistics   CHAPTER 3 Elements of probability   CHAPTER 4 Random variables and expectation   CHAPTER 5 Special random variables   CHAPTER 6 Distributions of sampling statistics   CHAPTER 7 Parameter estimation   CHAPTER 8 Hypothesis testing   CHAPTER 9 Regression   CHAPTER 10 Analysis of variance   CHAPTER 11 Goodness of fit tests and categorical data analysis   CHAPTER 12 Nonparametric hypothesis tests   CHAPTER 13 Quality control   CHAPTER 14 Life testing   CHAPTER 15 Simulation, bootstrap statistical methods, and permutation tests   CHAPTER 16 Machine learning and big data","brand":"Elsevier Science Publishing Co Inc","offers":[{"title":"Default Title","offer_id":49399840833879,"sku":"9780128243466","price":88.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780128243466.jpg?v=1730468881"},{"product_id":"dimension-theory-in-dynamical-systems-9780226662220","title":"Dimension Theory in Dynamical Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe principles of symmetry and self-symmetry are expressed in fractals, the subject of study in dimension theory. This book introduces an area of research which has recently appeared in the interface between dimension theory and the theory of dynamical systems, focusing on invariant fractals.","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":49400081482071,"sku":"9780226662220","price":30.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226662220.jpg?v=1730469655"},{"product_id":"introductory-statistics-with-r-9780387790534","title":"Introductory Statistics with R","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBasics.- The R environment.- Probability and distributions.- Descriptive statistics and graphics.- One- and two-sample tests.- Regression and correlation.- Analysis of variance and the KruskalWallis test.- Tabular data.- Power and the computation of sample size.- Advanced data handling.- Multiple regression.- Linear models.- Logistic regression.- Survival analysis.- Rates and Poisson regression.- Nonlinear curve fitting.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003eTECHNOMETRICS\u003c\/p\u003e\u003cp\u003e\"…extensive, well organized, and well documented…The book is an elegant R companion, suitable for the statistically initiated who want to program their own analyses. For experienced statisticians and data analysts, the book provides a good overview of the basic statistical analysis capabilities of R and presumably prepares readers for later migration to S…The format of this compact book is attractive…The book makes excellent use of fonts and intersperses graphics near the codes that produced them. Output from each procedure is dissected line by line to link R code with the computed result…I can recommend [this book] to its target audience. The author provides an excellent overview of R. I found the wealth of clear examples educational and a practical way to preview both R and S.\"\u003c\/p\u003e\u003cp\u003e\"The scope of the book, introductory statistics, is a very useful set of methods in parametric and non-parametric statistics up to logistic regression and survival analysis. … Where many constructs in R are very attractive for mathematical oriented users, e.g. matrices, Dalgaard succeeded in convincing me that with little extra effort they can be made very useful to less mathematically oriented people, e.g. by specifying row and column names, and proposing quite attractive ways to specify for example ‘subsets’ of rows and columns.\" (Dr. H. W. M. Hendriks, Kwantitatieve Methoden, Vol. 72B8, 2003)\u003c\/p\u003e\u003cp\u003e\"R is an Open Source implementation of the well-known S language. It works on multiple computing platforms and can be freely downloaded. R is thus ideally suited for teaching at many levels as well as for practical data analysis and methodological development. This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. … Brief sections introduce the statistical methods before they are used. A supplementary R package can be downloaded and contains the data sets.\" (Zentralblatt für Didaktik der Mathematik, August, 2004)\u003c\/p\u003e\u003cp\u003e\"This is a nice book on statistical methods and statistical computing in R, a language and environment for statistical computing and graphs: this dialect of the S language is available as free software through internet. … Explanation of statistical methods, together with an interpretation of statistical concepts, is the prevailing style of the text. They are illustrated by plenty of practical examples, all computed using R. This book will be useful for novices in applied statistics or in computing in R.\" (European Mathematical Society Newsletter, September, 2003)\u003c\/p\u003e\u003cp\u003e\"The book is an elegant R companion, suitable for the statistically initiated who want to program their own analyses. For experienced statisticians and data analysts, the book provides a good overview of the basic statistical analysis capabilities of R … prepares readers for later migration to S. … I can recommend Introductory Statistics With R to its target audience. The author provides an excellent overview of R. I found the wealth of clear examples educational and a practical way to preview both R and S.\" (Thomas D. Sandry, Technometrics, Vol. 45 (3), 2003)\u003c\/p\u003e\u003cp\u003e\"R is both a statistical computer environment and a programming language designed to perform statistical analysis and to produce adequate corresponding graphics. … The present book is … a very useful guide for introducing a number of basic concepts and techniques necessary to practical statistics, covering both elementary statistics and actual programming in the R language. The book is organized in 12 chapters and three appendices, each chapter ending with a beneficial section of proposed exercises.\" (Silvia Curteanu, Zentralblatt MATH, Vol. 1006, 2003)\u003c\/p\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“This review … roughly cover the introductory topics of a first year statistics course. The Introductory Statistics with R (ISwR) book is targeted for a biometric\/medical audience. It covers more topics … like multiple regression and survival analysis and expects the reader to know about basic statistics. … include examples and graphs together with the R code to construct them. … The ISwR book is good for an academic and biometric audience.” (Wolfgang Polasek, Statistical Papers, Vol. 52, 2011)\u003c\/p\u003e\u003cp\u003e“This is a welcome addition to the new edition that will be appreciated by its users. … The new edition is well written, and the new materials are well incorporated. Like the first edition, this edition will continue to be useful to the target audience, and I can safely recommend it to them.” (Technometrics, Vol. 51 (2), May, 2009)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasics. - The R environment. - Probability and statistics. - Descriptive statistics and graphics. - One and two sample tests. - Regression and correlation. - ANOVA and Kruskal-Wallis. - Tabular data. - Power and the computation of sample size. - Advanced data handling. - Multiple regression. - Linear models. - Logistic regression. - Survival analysis. - Rates and Poisson regression. - Nonlinear curve-fitting. - Obtaining and installing R and the ISwR package. - Data sets in the ISwR package. - Compendium. - Answers to exercises. - Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49401972752727,"sku":"9780387790534","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387790534.jpg?v=1730479007"},{"product_id":"the-mathematics-of-time-essays-on-dynamical-systems-economic-processes-and-related-topics-9780387905198","title":"The Mathematics of Time Essays On Dynamical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDifferentiable Dynamical Systems.- Notes.- References for Notes.- What Is Global Analysis?.- Stability and Genericity in Dynamical Systems.- Personal Perspectives on Mathematics and Mechanics.- Dynamics in General Equilibrium Theory.- Some Dynamical Questions in Mathematical Economics.- Review of Global Variational Analysis: Weier strass Integrals on a Riemannian Manifold.- Review of Catastrophe Theory: Selected Papers.- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff.- Robert Edward Bowen (jointly with J. Feldman and M. Ratner).- On How I Got Started in Dynamical Systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eDifferentiable Dynamical Systems.- Notes.- References for Notes.- What Is Global Analysis?.- Stability and Genericity in Dynamical Systems.- Personal Perspectives on Mathematics and Mechanics.- Dynamics in General Equilibrium Theory.- Some Dynamical Questions in Mathematical Economics.- Review of Global Variational Analysis: Weier strass Integrals on a Riemannian Manifold.- Review of Catastrophe Theory: Selected Papers.- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff.- Robert Edward Bowen (jointly with J. Feldman and M. Ratner).- On How I Got Started in Dynamical Systems.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49401973178711,"sku":"9780387905198","price":66.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"elementary-probability-theory-9780387955780","title":"Elementary Probability Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1 Set.- 1.1 Sample sets.- 1.2 Operations with sets.- 1.3 Various relations.- 1.4 Indicator.- Exercises.- 2 Probability.- 2.1 Examples of probability.- 2.2 Definition and illustrations.- 2.3 Deductions from the axioms.- 2.4 Independent events.- 2.5 Arithmetical density.- Exercises.- 3 Counting.- 3.1 Fundamental rule.- 3.2 Diverse ways of sampling.- 3.3 Allocation models; binomial coefficients.- 3.4 How to solve it.- Exercises.- 4 Random Variables.- 4.1 What is a random variable?.- 4.2 How do random variables come about?.- 4.3 Distribution and expectation.- 4.4 Integer-valued random variables.- 4.5 Random variables with densities.- 4.6 General case.- Exercises.- Appendix 1: Borel Fields and General Random Variables.- 5 Conditioning and Independence.- 5.1 Examples of conditioning.- 5.2 Basic formulas.- 5.3 Sequential sampling.- 5.4 Pólya's urn scheme.- 5.5 Independence and relevance.- 5.6 Genetical models.- Exercises.- 6 Mean, Variance, and Transforms.- 6.1 Basic properties of expectation\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"In spite of the original edition of the book being nearly thirty years old, the text still has its role to play in first and second year undergraduate probability courses. It provides an excellent foundation to more advanced courses in the subject.\"\u003cbr\u003e\u003cem\u003eShort Book Reviews, Vol. 23\/3, Dec. 2003\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\"This edition is the third revision of a text on mathematical probability first published in 1974. The text is aimed at undergraduate mathematics students and is accessible to a general audience. The prose is accurate, entertaining, and dense with historical tidbits. Two concluding chapters on mathematical finance have been added to the eight chapters in the third edition by the second author.\" The American Statistician, May 2004\u003c\/p\u003e \u003cp\u003eFrom the reviews of the fourth edition: \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"The main novelty in the fourth edition of this well-written book is the addition of new chapters … . The new chapters share the friendly yet rigorous style of the former ones. They begin with an account of the financial vocabulary, which is then expounded in probabilistic terms. … Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study.\" (Ricardo Maronna, Statistical Papers, Vol. 45 (4), 2004)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eSet * Probability * Counting * Random Variables * Conditioning and Independence * Mean, Variance and Transforms * Poisson and Normal Distributions * From Random Walks to Markov Chains * Mean-Variance Pricing Model * Option Pricing Theory","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49401973440855,"sku":"9780387955780","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387955780.jpg?v=1730479011"},{"product_id":"lq-dynamic-optimization-and-differential-games-9780470015247","title":"LQ Dynamic Optimization and Differential Games","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eLinear Quadratic Differential Games is an assessment of the state of the art in its field and modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eNotation and symbols.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Historical perspective.\u003c\/p\u003e \u003cp\u003e1.2 How to use this book.\u003c\/p\u003e \u003cp\u003e1.3 Outline of this book.\u003c\/p\u003e \u003cp\u003e1.4 Notes and references.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear algebra.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Basic concepts in linear algebra.\u003c\/p\u003e \u003cp\u003e2.2 Eigenvalues and eigenvectors.\u003c\/p\u003e \u003cp\u003e2.3 Complex eigenvalues.\u003c\/p\u003e \u003cp\u003e2.4 Cayley–Hamilton theorem.\u003c\/p\u003e \u003cp\u003e2.5 Invariant subspaces and Jordan canonical form.\u003c\/p\u003e \u003cp\u003e2.6 Semi-definite matrices.\u003c\/p\u003e \u003cp\u003e2.7 Algebraic Riccati equations.\u003c\/p\u003e \u003cp\u003e2.8 Notes and references.\u003c\/p\u003e \u003cp\u003e2.9 Exercises.\u003c\/p\u003e \u003cp\u003e2.10 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Dynamical systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Description of linear dynamical systems.\u003c\/p\u003e \u003cp\u003e3.2 Existence–uniqueness results for differential equations.\u003c\/p\u003e \u003cp\u003e3.2.1 General case.\u003c\/p\u003e \u003cp\u003e3.2.2 Control theoretic extensions.\u003c\/p\u003e \u003cp\u003e3.3 Stability theory: general case.\u003c\/p\u003e \u003cp\u003e3.4 Stability theory of planar systems.\u003c\/p\u003e \u003cp\u003e3.5 Geometric concepts.\u003c\/p\u003e \u003cp\u003e3.6 Performance specifications.\u003c\/p\u003e \u003cp\u003e3.7 Examples of differential games.\u003c\/p\u003e \u003cp\u003e3.8 Information, commitment and strategies.\u003c\/p\u003e \u003cp\u003e3.9 Notes and references.\u003c\/p\u003e \u003cp\u003e3.10 Exercises.\u003c\/p\u003e \u003cp\u003e3.11 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Optimization techniques.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Optimization of functions.\u003c\/p\u003e \u003cp\u003e4.2 The Euler–Lagrange equation.\u003c\/p\u003e \u003cp\u003e4.3 Pontryagin’s maximum principle.\u003c\/p\u003e \u003cp\u003e4.4 Dynamic programming principle.\u003c\/p\u003e \u003cp\u003e4.5 Solving optimal control problems.\u003c\/p\u003e \u003cp\u003e4.6 Notes and references.\u003c\/p\u003e \u003cp\u003e4.7 Exercises.\u003c\/p\u003e \u003cp\u003e4.8 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Regular linear quadratic optimal control.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Problem statement.\u003c\/p\u003e \u003cp\u003e5.2 Finite-planning horizon.\u003c\/p\u003e \u003cp\u003e5.3 Riccati differential equations.\u003c\/p\u003e \u003cp\u003e5.4 Infinite-planning horizon.\u003c\/p\u003e \u003cp\u003e5.5 Convergence results.\u003c\/p\u003e \u003cp\u003e5.6 Notes and references.\u003c\/p\u003e \u003cp\u003e5.7 Exercises.\u003c\/p\u003e \u003cp\u003e5.8 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Cooperative games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Pareto solutions.\u003c\/p\u003e \u003cp\u003e6.2 Bargaining concepts.\u003c\/p\u003e \u003cp\u003e6.3 Nash bargaining solution.\u003c\/p\u003e \u003cp\u003e6.4 Numerical solution.\u003c\/p\u003e \u003cp\u003e6.5 Notes and references.\u003c\/p\u003e \u003cp\u003e6.6 Exercises.\u003c\/p\u003e \u003cp\u003e6.7 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Non-cooperative open-loop information games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction.\u003c\/p\u003e \u003cp\u003e7.2 Finite-planning horizon.\u003c\/p\u003e \u003cp\u003e7.3 Open-loop Nash algebraic Riccati equations.\u003c\/p\u003e \u003cp\u003e7.4 Infinite-planning horizon.\u003c\/p\u003e \u003cp\u003e7.5 Computational aspects and illustrative examples.\u003c\/p\u003e \u003cp\u003e7.6 Convergence results.\u003c\/p\u003e \u003cp\u003e7.7 Scalar case.\u003c\/p\u003e \u003cp\u003e7.8 Economics examples.\u003c\/p\u003e \u003cp\u003e7.8.1 A simple government debt stabilization game.\u003c\/p\u003e \u003cp\u003e7.8.2 A game on dynamic duopolistic competition.\u003c\/p\u003e \u003cp\u003e7.9 Notes and references.\u003c\/p\u003e \u003cp\u003e7.10 Exercises.\u003c\/p\u003e \u003cp\u003e7.11 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Non-cooperative feedback information games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction.\u003c\/p\u003e \u003cp\u003e8.2 Finite-planning horizon.\u003c\/p\u003e \u003cp\u003e8.3 Infinite-planning horizon.\u003c\/p\u003e \u003cp\u003e8.4 Two-player scalar case.\u003c\/p\u003e \u003cp\u003e8.5 Computational aspects.\u003c\/p\u003e \u003cp\u003e8.5.1 Preliminaries.\u003c\/p\u003e \u003cp\u003e8.5.2 A scalar numerical algorithm: the two-player case.\u003c\/p\u003e \u003cp\u003e8.5.3 The N-player scalar case.\u003c\/p\u003e \u003cp\u003e8.6 Convergence results for the two-player scalar case.\u003c\/p\u003e \u003cp\u003e8.7 Notes and references.\u003c\/p\u003e \u003cp\u003e8.8 Exercises.\u003c\/p\u003e \u003cp\u003e8.9 Appendix.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Uncertain non-cooperative feedback information games.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Stochastic approach.\u003c\/p\u003e \u003cp\u003e9.2 Deterministic approach: introduction.\u003c\/p\u003e \u003cp\u003e9.3 The one-player case.\u003c\/p\u003e \u003cp\u003e9.4 The one-player scalar case.\u003c\/p\u003e \u003cp\u003e9.5 The two-player case.\u003c\/p\u003e \u003cp\u003e9.6 A fishery management game.\u003c\/p\u003e \u003cp\u003e9.7 A scalar numerical algorithm.\u003c\/p\u003e \u003cp\u003e9.8 Stochastic interpretation.\u003c\/p\u003e \u003cp\u003e9.9 Notes and references.\u003c\/p\u003e \u003cp\u003e9.10 Exercises.\u003c\/p\u003e \u003cp\u003e9.11 Appendix.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402254262615,"sku":"9780470015247","price":101.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470015247.jpg?v=1730479847"},{"product_id":"modeling-random-processes-for-engineers-and-managers-9780470322550","title":"Modeling Random Processes for Engineers and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eModeling Random Processes for Engineers and Managers\u003c\/i\u003e provides students with a gentle introduction to stochastic processes, emphasizing full explanations and many examples rather than formal mathematical theorems and proofs. The text offers an accessible entry into a very useful and versatile set of tools for dealing with uncertainty and variation. Many practical examples of models, as well as complete explanations of the thought process required to create them, motivate the presentation of the computational methods. In addition, the text contains a previously unpublished computational approach to solving many of the equations that occur in Markov processes. \u003ci\u003eModeling Random Processes\u003c\/i\u003e is intended to serve as an introduction, but more advanced students can use the case studies and problems to expand their understanding of practical uses of the theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Probability Review 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Interpreting and Using Probabilities 2\u003c\/p\u003e \u003cp\u003e1.2 Sample Spaces and Events 3\u003c\/p\u003e \u003cp\u003e1.3 Probability 4\u003c\/p\u003e \u003cp\u003e1.4 Random Variables 6\u003c\/p\u003e \u003cp\u003e1.5 Probability Distributions 6\u003c\/p\u003e \u003cp\u003e1.6 Joint, Marginal, and Conditional Distributions 11\u003c\/p\u003e \u003cp\u003e1.7 Expectation 14\u003c\/p\u003e \u003cp\u003e1.8 Variance and Other Moments 16\u003c\/p\u003e \u003cp\u003e1.9 The Law of Total Probability 18\u003c\/p\u003e \u003cp\u003e1.10 Discrete Probability Distributions 20\u003c\/p\u003e \u003cp\u003e1.11 Continuous Probability Distributions 23\u003c\/p\u003e \u003cp\u003e1.12 Where Do Distributions Come From? 26\u003c\/p\u003e \u003cp\u003e1.13 The Binomial Process 28\u003c\/p\u003e \u003cp\u003e1.14 Recommended Reading 29\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Formulating Markov Chain Models 32\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 An Example 33\u003c\/p\u003e \u003cp\u003e2.2 Modeling the Progress of Time 34\u003c\/p\u003e \u003cp\u003e2.3 Modeling Possibilities as States 36\u003c\/p\u003e \u003cp\u003e2.4 Simplifying Assumptions 38\u003c\/p\u003e \u003cp\u003e2.5 Modeling Changes of State as Transitions 40\u003c\/p\u003e \u003cp\u003e2.6 Obtaining the Data 45\u003c\/p\u003e \u003cp\u003e2.7 Another Example 46\u003c\/p\u003e \u003cp\u003e2.8 A Case Study 47\u003c\/p\u003e \u003cp\u003e2.9 Higher Order Markov Chains 50\u003c\/p\u003e \u003cp\u003e2.10 Reducing the Number of States 52\u003c\/p\u003e \u003cp\u003e2.11 Nonstationary Markov Chains 53\u003c\/p\u003e \u003cp\u003e2.12 Other Example 54\u003c\/p\u003e \u003cp\u003e2.13 Summary 67\u003c\/p\u003e \u003cp\u003e2.14 Recommended Reading 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Markov Chain Calculations 72\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Walk Probabilities 73\u003c\/p\u003e \u003cp\u003e3.2 Transition Probabilities 74\u003c\/p\u003e \u003cp\u003e3.3 State Probabilities 78\u003c\/p\u003e \u003cp\u003e3.4 A Numerical Example 79\u003c\/p\u003e \u003cp\u003e3.5 Expected Number of Visits 80\u003c\/p\u003e \u003cp\u003e3.6 Sojourn Times 82\u003c\/p\u003e \u003cp\u003e3.7 First Passage and Return Probabilities 83\u003c\/p\u003e \u003cp\u003e3.8 Computational Formulas for All Markov Chains 86\u003c\/p\u003e \u003cp\u003e3.9 Special Classes of Markov Chains 86\u003c\/p\u003e \u003cp\u003e3.10 Steady-State Probabilities 87\u003c\/p\u003e \u003cp\u003e3.11 The Uses of Steady-State Results 92\u003c\/p\u003e \u003cp\u003e3.12 Mean First Passage Times 93\u003c\/p\u003e \u003cp\u003e3.13 Computational Formulas for Ergodic Markov Chains 96\u003c\/p\u003e \u003cp\u003e3.14 Terminating Markov Chains 96\u003c\/p\u003e \u003cp\u003e3.15 Expected Number of Visits 98\u003c\/p\u003e \u003cp\u003e3.16 Expected Duration of a Terminating Process 99\u003c\/p\u003e \u003cp\u003e3.17 Absorption Probabilities 100\u003c\/p\u003e \u003cp\u003e3.18 Hit Probabilities 102\u003c\/p\u003e \u003cp\u003e3.19 Conditional Mean First Passage Times to Absorbing States 103\u003c\/p\u003e \u003cp\u003e3.20 Computational Formulas for Terminating Processes 105\u003c\/p\u003e \u003cp\u003e3.21 Call Center Calculations 105\u003c\/p\u003e \u003cp\u003e3.22 Classification Terminology 106\u003c\/p\u003e \u003cp\u003e3.23 Additional Complications in Infinite Chains 111\u003c\/p\u003e \u003cp\u003e3.24 Dealing with a Reducible Process 112\u003c\/p\u003e \u003cp\u003e3.25 Periodic Chains 113\u003c\/p\u003e \u003cp\u003e3.26 Ergodic Chains 114\u003c\/p\u003e \u003cp\u003e3.27 Recommended Reading 115\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Rewards on Markov Chains 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Formulation 120\u003c\/p\u003e \u003cp\u003e4.2 A Numerical Example 120\u003c\/p\u003e \u003cp\u003e4.3 Expected Total Reward 121\u003c\/p\u003e \u003cp\u003e4.4 Random Variable Rewards 124\u003c\/p\u003e \u003cp\u003e4.5 Semi-Markov Processes 126\u003c\/p\u003e \u003cp\u003e4.6 Limiting Results for Ergodic Processes 126\u003c\/p\u003e \u003cp\u003e4.7 Total Reward for Terminating Processes 130\u003c\/p\u003e \u003cp\u003e4.8 Case Study 132\u003c\/p\u003e \u003cp\u003e4.9 Discounting 133\u003c\/p\u003e \u003cp\u003e4.10 Case Study 135\u003c\/p\u003e \u003cp\u003e4.11 Recommended Reading 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Continuous Time Markov Processes 140\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 An Example 141\u003c\/p\u003e \u003cp\u003e5.2 Interpreting Transition Rates 146\u003c\/p\u003e \u003cp\u003e5.3 The Assumptions Reconsidered 149\u003c\/p\u003e \u003cp\u003e5.4 Aging Does Not Affect the Transition Time 150\u003c\/p\u003e \u003cp\u003e5.5 Competing Transitions 152\u003c\/p\u003e \u003cp\u003e5.6 Sojourn Times 153\u003c\/p\u003e \u003cp\u003e5.7 Embedded Markov Chains 154\u003c\/p\u003e \u003cp\u003e5.8 Deriving the Differential Equations 155\u003c\/p\u003e \u003cp\u003e5.9 Solving the Differential Equations 157\u003c\/p\u003e \u003cp\u003e5.10 State Probabilities 159\u003c\/p\u003e \u003cp\u003e5.11 First Passage Probability Functions 159\u003c\/p\u003e \u003cp\u003e5.12 State Classification 160\u003c\/p\u003e \u003cp\u003e5.13 Steady-State Probabilities 161\u003c\/p\u003e \u003cp\u003e5.14 Other Computable Quantities 163\u003c\/p\u003e \u003cp\u003e5.15 Case Study 165\u003c\/p\u003e \u003cp\u003e5.16 Birth-Death Processes 167\u003c\/p\u003e \u003cp\u003e5.17 The Poisson Process 169\u003c\/p\u003e \u003cp\u003e5.18 Properties of Poisson Processes 171\u003c\/p\u003e \u003cp\u003e5.19 Khintchine’s Theorem 172\u003c\/p\u003e \u003cp\u003e5.20 Phase-Type Distributions 173\u003c\/p\u003e \u003cp\u003e5.21 Conclusions 175\u003c\/p\u003e \u003cp\u003e5.22 Recommended Reading 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Queueing Models 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 An Example 180\u003c\/p\u003e \u003cp\u003e6.2 General Characteristics 182\u003c\/p\u003e \u003cp\u003e6.3 Performance Measures 186\u003c\/p\u003e \u003cp\u003e6.4 Relations Among Performance Measures 188\u003c\/p\u003e \u003cp\u003e6.5 Little’s Formula 190\u003c\/p\u003e \u003cp\u003e6.6 Markovian Queueing Models 191\u003c\/p\u003e \u003cp\u003e6.7 The M\/M\/1 Model 193\u003c\/p\u003e \u003cp\u003e6.8 The Significance of Traffic Intensity 198\u003c\/p\u003e \u003cp\u003e6.9 Unnormalized Solutions 200\u003c\/p\u003e \u003cp\u003e6.10 Limited Queue Capacity 202\u003c\/p\u003e \u003cp\u003e6.11 Multiple Servers 204\u003c\/p\u003e \u003cp\u003e6.12 Is It Better to Merge or Separate Servers? 207\u003c\/p\u003e \u003cp\u003e6.13 Which is Better: More Servers or Faster Servers 208\u003c\/p\u003e \u003cp\u003e6.14 Case Study: A Grain Elevator 209\u003c\/p\u003e \u003cp\u003e6.15 The M\/M\/c\/c and M\/M\/1 Models 210\u003c\/p\u003e \u003cp\u003e6.16 Finite Sources 212\u003c\/p\u003e \u003cp\u003e6.17 The Machine Repairmen Model 214\u003c\/p\u003e \u003cp\u003e6.18 Numerical Calculations Using a Spreadsheet 214\u003c\/p\u003e \u003cp\u003e6.19 Queue Discipline Variations 217\u003c\/p\u003e \u003cp\u003e6.20 Non-Markovian Queues 218\u003c\/p\u003e \u003cp\u003e6.21 The M\/G\/1 Model 219\u003c\/p\u003e \u003cp\u003e6.22 Approximate Solutions for Other Models 220\u003c\/p\u003e \u003cp\u003e6.23 Conclusion 221\u003c\/p\u003e \u003cp\u003e6.24 Recommended Reading 221\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Networks of Queues 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Open Networks of Markovian Queues 226\u003c\/p\u003e \u003cp\u003e7.2 An Example Open Network 227\u003c\/p\u003e \u003cp\u003e7.3 Extensions 228\u003c\/p\u003e \u003cp\u003e7.4 Closed Networks 229\u003c\/p\u003e \u003cp\u003e7.5 A Preliminary Example 229\u003c\/p\u003e \u003cp\u003e7.6 Relative Arrival Rates 230\u003c\/p\u003e \u003cp\u003e7.7 Unnormalized Solutions for Individual Stations 232\u003c\/p\u003e \u003cp\u003e7.8 Assembling the Pieces of the Solution 234\u003c\/p\u003e \u003cp\u003e7.9 Calculating the Normalization Constant 235\u003c\/p\u003e \u003cp\u003e7.10 Performance Measures for Closed Networks 237\u003c\/p\u003e \u003cp\u003e7.11 Creating a Closed Model 239\u003c\/p\u003e \u003cp\u003e7.12 Case Study 242\u003c\/p\u003e \u003cp\u003e7.13 Extensions 247\u003c\/p\u003e \u003cp\u003e7.14 Approximate Methods 247\u003c\/p\u003e \u003cp\u003e7.15 Recommended Reading 248\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Using the Transition Diagram to Compute 251\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 An Example 252\u003c\/p\u003e \u003cp\u003e8.2 Definitions 254\u003c\/p\u003e \u003cp\u003e8.3 Steady-State Probabilities 258\u003c\/p\u003e \u003cp\u003e8.4 How to Generate All In-trees 259\u003c\/p\u003e \u003cp\u003e8.5 Check Your Understanding 262\u003c\/p\u003e \u003cp\u003e8.6 Generalization to Other Quantities 263\u003c\/p\u003e \u003cp\u003e8.7 Mean First Passage Times 264\u003c\/p\u003e \u003cp\u003e8.8 Results for Terminating Processes 265\u003c\/p\u003e \u003cp\u003e8.9 How to Simplify the Arithmetic 266\u003c\/p\u003e \u003cp\u003e8.10 How to Systematically Generate r-Forests 267\u003c\/p\u003e \u003cp\u003e8.11 Summary of Results 267\u003c\/p\u003e \u003cp\u003e8.12 How to Remember the Formulas 268\u003c\/p\u003e \u003cp\u003e8.13 Advanced Topics 268\u003c\/p\u003e \u003cp\u003e8.14 Recommended Reading 269\u003c\/p\u003e \u003cp\u003eAppendix 1 271\u003c\/p\u003e \u003cp\u003eAppendix 2 278\u003c\/p\u003e \u003cp\u003eIndex 300\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402315145559,"sku":"9780470322550","price":170.81,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470322550.jpg?v=1730480043"},{"product_id":"stochastic-geometry-and-its-applications-9780470664810","title":"Stochastic Geometry and Its Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn extensive update to a classic text     Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eForeword to the first edition xiii\u003c\/p\u003e \u003cp\u003eFrom the preface to the first edition xvii\u003c\/p\u003e \u003cp\u003ePreface to the second edition xix\u003c\/p\u003e \u003cp\u003ePreface to the third edition xxi\u003c\/p\u003e \u003cp\u003eNotation xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Mathematical foundations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Set theory 1\u003c\/p\u003e \u003cp\u003e1.2 Topology in Euclidean spaces 3\u003c\/p\u003e \u003cp\u003e1.3 Operations on subsets of Euclidean space 5\u003c\/p\u003e \u003cp\u003e1.4 Mathematical morphology and image analysis 7\u003c\/p\u003e \u003cp\u003e1.5 Euclidean isometries 9\u003c\/p\u003e \u003cp\u003e1.6 Convex sets in Euclidean spaces 10\u003c\/p\u003e \u003cp\u003e1.7 Functions describing convex sets 17\u003c\/p\u003e \u003cp\u003e1.8 Polyconvex sets 24\u003c\/p\u003e \u003cp\u003e1.9 Measure and integration theory 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Point processes I: The Poisson point process 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 35\u003c\/p\u003e \u003cp\u003e2.2 The binomial point process 36\u003c\/p\u003e \u003cp\u003e2.3 The homogeneous Poisson point process 41\u003c\/p\u003e \u003cp\u003e2.4 The inhomogeneous and general Poisson point process 51\u003c\/p\u003e \u003cp\u003e2.5 Simulation of Poisson point processes 53\u003c\/p\u003e \u003cp\u003e2.6 Statistics for the homogeneous Poisson point process 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Random closed sets I: The Boolean model 64\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction and basic properties 64\u003c\/p\u003e \u003cp\u003e3.2 The Boolean model with convex grains 78\u003c\/p\u003e \u003cp\u003e3.3 Coverage and connectivity 89\u003c\/p\u003e \u003cp\u003e3.4 Statistics 95\u003c\/p\u003e \u003cp\u003e3.5 Generalisations and variations 103\u003c\/p\u003e \u003cp\u003e3.6 Hints for practical applications 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Point processes II: General theory 108\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Basic properties 108\u003c\/p\u003e \u003cp\u003e4.2 Marked point processes 116\u003c\/p\u003e \u003cp\u003e4.3 Moment measures and related quantities 120\u003c\/p\u003e \u003cp\u003e4.4 Palm distributions 127\u003c\/p\u003e \u003cp\u003e4.5 The second moment measure 139\u003c\/p\u003e \u003cp\u003e4.6 Summary characteristics 143\u003c\/p\u003e \u003cp\u003e4.7 Introduction to statistics for stationary spatial point processes 145\u003c\/p\u003e \u003cp\u003e4.8 General point processes 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Point processes III: Models 158\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Operations on point processes 158\u003c\/p\u003e \u003cp\u003e5.2 Doubly stochastic Poisson processes (Cox processes) 166\u003c\/p\u003e \u003cp\u003e5.3 Neyman–Scott processes 171\u003c\/p\u003e \u003cp\u003e5.4 Hard-core point processes 176\u003c\/p\u003e \u003cp\u003e5.5 Gibbs point processes 178\u003c\/p\u003e \u003cp\u003e5.6 Shot-noise fields 200\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Random closed sets II: The general case 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Basic properties 205\u003c\/p\u003e \u003cp\u003e6.2 Random compact sets 213\u003c\/p\u003e \u003cp\u003e6.3 Characteristics for stationary and isotropic random closed sets 216\u003c\/p\u003e \u003cp\u003e6.4 Nonparametric statistics for stationary random closed sets 230\u003c\/p\u003e \u003cp\u003e6.5 Germ–grain models 237\u003c\/p\u003e \u003cp\u003e6.6 Other random closed set models 255\u003c\/p\u003e \u003cp\u003e6.7 Stochastic reconstruction of random sets 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Random measures 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Fundamentals 279\u003c\/p\u003e \u003cp\u003e7.2 Moment measures and related characteristics 284\u003c\/p\u003e \u003cp\u003e7.3 Examples of random measures 286\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Line, fibre and surface processes 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 297\u003c\/p\u003e \u003cp\u003e8.2 Flat processes 302\u003c\/p\u003e \u003cp\u003e8.3 Planar fibre processes 314\u003c\/p\u003e \u003cp\u003e8.4 Spatial fibre processes 330\u003c\/p\u003e \u003cp\u003e8.5 Surface processes 333\u003c\/p\u003e \u003cp\u003e8.6 Marked fibre and surface processes 339\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Random tessellations, geometrical networks and graphs 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction and definitions 343\u003c\/p\u003e \u003cp\u003e9.2 Mathematical models for random tessellations 346\u003c\/p\u003e \u003cp\u003e9.3 General ideas and results for stationary planar tessellations 357\u003c\/p\u003e \u003cp\u003e9.4 Mean-value formulae for stationary spatial tessellations 367\u003c\/p\u003e \u003cp\u003e9.5 Poisson line and plane tessellations 370\u003c\/p\u003e \u003cp\u003e9.6 STIT tessellations 375\u003c\/p\u003e \u003cp\u003e9.7 Poisson-Voronoi and Delaunay tessellations 376\u003c\/p\u003e \u003cp\u003e9.8 Laguerre tessellations 386\u003c\/p\u003e \u003cp\u003e9.9 Johnson–Mehl tessellations 388\u003c\/p\u003e \u003cp\u003e9.10 Statistics for stationary tessellations 390\u003c\/p\u003e \u003cp\u003e9.11 Random geometrical networks 397\u003c\/p\u003e \u003cp\u003e9.12 Random graphs 402\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Stereology 411\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 411\u003c\/p\u003e \u003cp\u003e10.2 The fundamental mean-value formulae of stereology 413\u003c\/p\u003e \u003cp\u003e10.3 Stereological mean-value formulae for germ–grain models 421\u003c\/p\u003e \u003cp\u003e10.4 Stereological methods for spatial systems of balls 425\u003c\/p\u003e \u003cp\u003e10.5 Stereological problems for nonspherical grains (shape-and-size problems) 436\u003c\/p\u003e \u003cp\u003e10.6 Stereology for spatial tessellations 440\u003c\/p\u003e \u003cp\u003e10.7 Second-order characteristics and directional distributions 444\u003c\/p\u003e \u003cp\u003eReferences 453\u003c\/p\u003e \u003cp\u003eAuthor index 507\u003c\/p\u003e \u003cp\u003eSubject index 521\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402396082519,"sku":"9780470664810","price":76.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470664810.jpg?v=1730480274"},{"product_id":"stochastic-claims-reserving-methods-in-insurance-9780470723463","title":"Stochastic Claims Reserving Methods in Insurance","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCovers all the theory and practical advice that actuaries need in order to determine the claims reserves for non-life insurance. Describes all the necessary mathematical methods used to estimate loss reserves and shares the authors' practical experience, which is essential in showing which of the methods should be applied in any given situation.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgement xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction and Notation 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Claims process 1\u003c\/p\u003e \u003cp\u003e1.1.1 Accounting principles and accident years 2\u003c\/p\u003e \u003cp\u003e1.1.2 Inflation 3\u003c\/p\u003e \u003cp\u003e1.2 Structural framework to the claims-reserving problem 5\u003c\/p\u003e \u003cp\u003e1.2.1 Fundamental properties of the claims reserving process 7\u003c\/p\u003e \u003cp\u003e1.2.2 Known and unknown claims 9\u003c\/p\u003e \u003cp\u003e1.3 Outstanding loss liabilities, classical notation 10\u003c\/p\u003e \u003cp\u003e1.4 General remarks 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basic Methods 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Chain-ladder method (distribution-free) 15\u003c\/p\u003e \u003cp\u003e2.2 Bornhuetter–Ferguson method 21\u003c\/p\u003e \u003cp\u003e2.3 Number of IBNyR claims, Poisson model 25\u003c\/p\u003e \u003cp\u003e2.4 Poisson derivation of the CL algorithm 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Chain-Ladder Models 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Mean square error of prediction 33\u003c\/p\u003e \u003cp\u003e3.2 Chain-ladder method 36\u003c\/p\u003e \u003cp\u003e3.2.1 Mack model (distribution-free CL model) 37\u003c\/p\u003e \u003cp\u003e3.2.2 Conditional process variance 41\u003c\/p\u003e \u003cp\u003e3.2.3 Estimation error for single accident years 44\u003c\/p\u003e \u003cp\u003e3.2.4 Conditional MSEP, aggregated accident years 55\u003c\/p\u003e \u003cp\u003e3.3 Bounds in the unconditional approach 58\u003c\/p\u003e \u003cp\u003e3.3.1 Results and interpretation 58\u003c\/p\u003e \u003cp\u003e3.3.2 Aggregation of accident years 63\u003c\/p\u003e \u003cp\u003e3.3.3 Proof of Theorems 3.17, 3.18 and 3.20 64\u003c\/p\u003e \u003cp\u003e3.4 Analysis of error terms in the CL method 70\u003c\/p\u003e \u003cp\u003e3.4.1 Classical CL model 70\u003c\/p\u003e \u003cp\u003e3.4.2 Enhanced CL model 71\u003c\/p\u003e \u003cp\u003e3.4.3 Interpretation 72\u003c\/p\u003e \u003cp\u003e3.4.4 CL estimator in the enhanced model 73\u003c\/p\u003e \u003cp\u003e3.4.5 Conditional process and parameter prediction errors 74\u003c\/p\u003e \u003cp\u003e3.4.6 CL factors and parameter estimation error 75\u003c\/p\u003e \u003cp\u003e3.4.7 Parameter estimation 81\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Bayesian Models 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Benktander–Hovinen method and Cape–Cod model 91\u003c\/p\u003e \u003cp\u003e4.1.1 Benktander–Hovinen method 92\u003c\/p\u003e \u003cp\u003e4.1.2 Cape–Cod model 95\u003c\/p\u003e \u003cp\u003e4.2 Credible claims reserving methods 98\u003c\/p\u003e \u003cp\u003e4.2.1 Minimizing quadratic loss functions 98\u003c\/p\u003e \u003cp\u003e4.2.2 Distributional examples to credible claims reserving 101\u003c\/p\u003e \u003cp\u003e4.2.3 Log-normal\/Log-normal model 105\u003c\/p\u003e \u003cp\u003e4.3 Exact Bayesian models 113\u003c\/p\u003e \u003cp\u003e4.3.1 Overdispersed Poisson model with gamma prior distribution 114\u003c\/p\u003e \u003cp\u003e4.3.2 Exponential dispersion family with its associated conjugates 122\u003c\/p\u003e \u003cp\u003e4.4 Markov chain Monte Carlo methods 131\u003c\/p\u003e \u003cp\u003e4.5 Bühlmann–Straub credibility model 145\u003c\/p\u003e \u003cp\u003e4.6 Multidimensional credibility models 154\u003c\/p\u003e \u003cp\u003e4.6.1 Hachemeister regression model 155\u003c\/p\u003e \u003cp\u003e4.6.2 Other credibility models 159\u003c\/p\u003e \u003cp\u003e4.7 Kalman filter 160\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Distributional Models 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Log-normal model for cumulative claims 167\u003c\/p\u003e \u003cp\u003e5.1.1 Known variances σ\u003csub\u003ej\u003c\/sub\u003e \u003csup\u003e2\u003c\/sup\u003e 170\u003c\/p\u003e \u003cp\u003e5.1.2 Unknown variances 177\u003c\/p\u003e \u003cp\u003e5.2 Incremental claims 182\u003c\/p\u003e \u003cp\u003e5.2.1 (Overdispersed) Poisson model 182\u003c\/p\u003e \u003cp\u003e5.2.2 Negative-Binomial model 183\u003c\/p\u003e \u003cp\u003e5.2.3 Log-normal model for incremental claims 185\u003c\/p\u003e \u003cp\u003e5.2.4 Gamma model 186\u003c\/p\u003e \u003cp\u003e5.2.5 Tweedie’s compound Poisson model 188\u003c\/p\u003e \u003cp\u003e5.2.6 Wright’s model 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Generalized Linear Models 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Maximum likelihood estimators 201\u003c\/p\u003e \u003cp\u003e6.2 Generalized linear models framework 203\u003c\/p\u003e \u003cp\u003e6.3 Exponential dispersion family 205\u003c\/p\u003e \u003cp\u003e6.4 Parameter estimation in the EDF 208\u003c\/p\u003e \u003cp\u003e6.4.1 MLE for the EDF 208\u003c\/p\u003e \u003cp\u003e6.4.2 Fisher’s scoring method 210\u003c\/p\u003e \u003cp\u003e6.4.3 Mean square error of prediction 214\u003c\/p\u003e \u003cp\u003e6.5 Other GLM models 223\u003c\/p\u003e \u003cp\u003e6.6 Bornhuetter–Ferguson method, revisited 223\u003c\/p\u003e \u003cp\u003e6.6.1 MSEP in the BF method, single accident year 226\u003c\/p\u003e \u003cp\u003e6.6.2 MSEP in the BF method, aggregated accident years 230\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Bootstrap Methods 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 233\u003c\/p\u003e \u003cp\u003e7.1.1 Efron’s non-parametric bootstrap 234\u003c\/p\u003e \u003cp\u003e7.1.2 Parametric bootstrap 236\u003c\/p\u003e \u003cp\u003e7.2 Log-normal model for cumulative sizes 237\u003c\/p\u003e \u003cp\u003e7.3 Generalized linear models 242\u003c\/p\u003e \u003cp\u003e7.4 Chain-ladder method 244\u003c\/p\u003e \u003cp\u003e7.4.1 Approach 1: Unconditional estimation error 246\u003c\/p\u003e \u003cp\u003e7.4.2 Approach 3: Conditional estimation error 247\u003c\/p\u003e \u003cp\u003e7.5 Mathematical thoughts about bootstrapping methods 248\u003c\/p\u003e \u003cp\u003e7.6 Synchronous bootstrapping of seemingly unrelated regressions 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Multivariate Reserving Methods 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 General multivariate framework 257\u003c\/p\u003e \u003cp\u003e8.2 Multivariate chain-ladder method 259\u003c\/p\u003e \u003cp\u003e8.2.1 Multivariate CL model 259\u003c\/p\u003e \u003cp\u003e8.2.2 Conditional process variance 264\u003c\/p\u003e \u003cp\u003e8.2.3 Conditional estimation error for single accident years 265\u003c\/p\u003e \u003cp\u003e8.2.4 Conditional MSEP, aggregated accident years 272\u003c\/p\u003e \u003cp\u003e8.2.5 Parameter estimation 274\u003c\/p\u003e \u003cp\u003e8.3 Multivariate additive loss reserving method 288\u003c\/p\u003e \u003cp\u003e8.3.1 Multivariate additive loss reserving model 288\u003c\/p\u003e \u003cp\u003e8.3.2 Conditional process variance 295\u003c\/p\u003e \u003cp\u003e8.3.3 Conditional estimation error for single accident years 295\u003c\/p\u003e \u003cp\u003e8.3.4 Conditional MSEP, aggregated accident years 297\u003c\/p\u003e \u003cp\u003e8.3.5 Parameter estimation 299\u003c\/p\u003e \u003cp\u003e8.4 Combined Multivariate CL and ALR method 308\u003c\/p\u003e \u003cp\u003e8.4.1 Combined CL and ALR method: the model 308\u003c\/p\u003e \u003cp\u003e8.4.2 Conditional cross process variance 313\u003c\/p\u003e \u003cp\u003e8.4.3 Conditional cross estimation error for single accident years 315\u003c\/p\u003e \u003cp\u003e8.4.4 Conditional MSEP, aggregated accident years 319\u003c\/p\u003e \u003cp\u003e8.4.5 Parameter estimation 321\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Selected Topics I: Chain-Ladder Methods 331\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Munich chain-ladder 331\u003c\/p\u003e \u003cp\u003e9.1.1 The Munich chain-ladder model 333\u003c\/p\u003e \u003cp\u003e9.1.2 Credibility approach to the MCL method 335\u003c\/p\u003e \u003cp\u003e9.1.3 MCL Parameter estimation 340\u003c\/p\u003e \u003cp\u003e9.2 CL Reserving: A Bayesian inference model 346\u003c\/p\u003e \u003cp\u003e9.2.1 Prediction of the ultimate claim 351\u003c\/p\u003e \u003cp\u003e9.2.2 Likelihood function and posterior distribution 351\u003c\/p\u003e \u003cp\u003e9.2.3 Mean square error of prediction 354\u003c\/p\u003e \u003cp\u003e9.2.4 Credibility chain-ladder 359\u003c\/p\u003e \u003cp\u003e9.2.5 Examples 361\u003c\/p\u003e \u003cp\u003e9.2.6 Markov chain Monte Carlo methods 364\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Selected Topics II: Individual Claims Development Processes 369\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Modelling claims development processes for individual claims 369\u003c\/p\u003e \u003cp\u003e10.1.1 Modelling framework 370\u003c\/p\u003e \u003cp\u003e10.1.2 Claims reserving categories 376\u003c\/p\u003e \u003cp\u003e10.2 Separating IBNeR and IBNyR claims 379\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Statistical Diagnostics 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Testing age-to-age factors 391\u003c\/p\u003e \u003cp\u003e11.1.1 Model choice 394\u003c\/p\u003e \u003cp\u003e11.1.2 Age-to-age factors 396\u003c\/p\u003e \u003cp\u003e11.1.3 Homogeneity in time and distributional assumptions 398\u003c\/p\u003e \u003cp\u003e11.1.4 Correlations 399\u003c\/p\u003e \u003cp\u003e11.1.5 Diagonal effects 401\u003c\/p\u003e \u003cp\u003e11.2 Non-parametric smoothing 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Distributions 405\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Discrete distributions 405\u003c\/p\u003e \u003cp\u003eA.1.1 Binomial distribution 405\u003c\/p\u003e \u003cp\u003eA.1.2 Poisson distribution 405\u003c\/p\u003e \u003cp\u003eA.1.3 Negative-Binomial distribution 405\u003c\/p\u003e \u003cp\u003eA.2 Continuous distributions 406\u003c\/p\u003e \u003cp\u003eA.2.1 Uniform distribution 406\u003c\/p\u003e \u003cp\u003eA.2.2 Normal distribution 406\u003c\/p\u003e \u003cp\u003eA.2.3 Log-normal distribution 407\u003c\/p\u003e \u003cp\u003eA.2.4 Gamma distribution 407\u003c\/p\u003e \u003cp\u003eA.2.5 Beta distribution 408\u003c\/p\u003e \u003cp\u003eBibliography 409\u003c\/p\u003e \u003cp\u003eIndex 417\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402418987351,"sku":"9780470723463","price":78.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470723463.jpg?v=1730480340"},{"product_id":"levy-processes-in-credit-risk-9780470743065","title":"Levy Processes in Credit Risk","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eLevy Processes in Credit Risk  is an introductory guide to using Levy processes for credit risk modelling, covering all types of credit derivatives: from the single name vanillas such as CDSs right through to structured credit risk products such as CPPIs and CPDOs.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This text introduces into the use of Levy processes in credit risk modeling. After a general overview of credit risk and standard credit derivatives, the authors provide a short introduction into Levy processes in general. This material is then used to study single-name credit derivatives. Following this, the authors introduce into firm-value Levy models, including the Merton model, Black-Cox model, Levy first passage model, variance gamma model and the one sided Levy default model. The problem of calibration is discussed. After that, the authors introduce intensity Levy models such as the Jarrow and Turnbull model, the Cox model and the intensity-OU model. Multivariate credit products, collateralized debt obligations and multivariate index modeling are discussed in the following. In the final part of their book, the authors study credit CPPIs and CPDOs as well as asset-backed securities.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2010)\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePreface.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eAcknowledgements.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePART I: INTRODUCTION.\u003c\/p\u003e \u003cp\u003e1 An Introduction to Credit Risk.\u003c\/p\u003e \u003cp\u003e1.1 Credit Risk.\u003c\/p\u003e \u003cp\u003e1.1.1 Historical and Risk-Neutral Probabilities.\u003c\/p\u003e \u003cp\u003e1.1.2 Bond Prices and Default Probability.\u003c\/p\u003e \u003cp\u003e1.2 Credit Risk Modelling.\u003c\/p\u003e \u003cp\u003e1.3 Credit Derivatives.\u003c\/p\u003e \u003cp\u003e1.4 Modelling Assumptions.\u003c\/p\u003e \u003cp\u003e1.4.1 Probability Space and Filtrations.\u003c\/p\u003e \u003cp\u003e1.4.2 The Risk-Free Asset.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 An Introduction to Lévy Processes.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Brownian Motion.\u003c\/p\u003e \u003cp\u003e2.2 Lévy Processes.\u003c\/p\u003e \u003cp\u003e2.3 Examples of Lévy Processes.\u003c\/p\u003e \u003cp\u003e2.3.1 Poisson Process.\u003c\/p\u003e \u003cp\u003e2.3.2 Compound Poisson Process.\u003c\/p\u003e \u003cp\u003e2.3.3 The Gamma Process.\u003c\/p\u003e \u003cp\u003e2.3.4 Inverse Gaussian Process.\u003c\/p\u003e \u003cp\u003e2.3.5 The CMY Process.\u003c\/p\u003e \u003cp\u003e2.3.6 The Variance Gamma Process.\u003c\/p\u003e \u003cp\u003e2.4 Ornstein–Uhlenbeck Processes.\u003c\/p\u003e \u003cp\u003e2.4.1 The Gamma-OU Process.\u003c\/p\u003e \u003cp\u003e2.4.2 The Inverse Gaussian-OU Process.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II: SINGLE-NAME MODELLING.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3 Single-Name Credit Derivatives.\u003c\/p\u003e \u003cp\u003e3.1 Credit Default Swaps.\u003c\/p\u003e \u003cp\u003e3.1.1 Credit Default Swaps Pricing.\u003c\/p\u003e \u003cp\u003e3.1.2 Calibration Assumptions.\u003c\/p\u003e \u003cp\u003e3.2 Credit Default Swap Forwards.\u003c\/p\u003e \u003cp\u003e3.2.1 Credit Default Swap Forward Pricing.\u003c\/p\u003e \u003cp\u003e3.3 Constant Maturity Credit Default Swaps.\u003c\/p\u003e \u003cp\u003e3.3.1 Constant Maturity Credit Default Swaps Pricing.\u003c\/p\u003e \u003cp\u003e3.4 Options on CDS.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Firm-Value Lévy Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The Merton Model.\u003c\/p\u003e \u003cp\u003e4.2 The Black–Cox Model with Constant Barrier.\u003c\/p\u003e \u003cp\u003e4.3 The Lévy First-Passage Model.\u003c\/p\u003e \u003cp\u003e4.4 The Variance Gamma Model.\u003c\/p\u003e \u003cp\u003e4.4.1 Sensitivity to the Parameters.\u003c\/p\u003e \u003cp\u003e4.4.2 Calibration on CDS Term Structure Curve.\u003c\/p\u003e \u003cp\u003e4.5 One-Sided Lévy Default Model.\u003c\/p\u003e \u003cp\u003e4.5.1 Wiener–Hopf Factorization and Default Probabilities.\u003c\/p\u003e \u003cp\u003e4.5.2 Illustration of the Pricing of Credit Default Swaps.\u003c\/p\u003e \u003cp\u003e4.6 Dynamic Spread Generator.\u003c\/p\u003e \u003cp\u003e4.6.1 Generating Spread Paths.\u003c\/p\u003e \u003cp\u003e4.6.2 Pricing of Options on CDSs.\u003c\/p\u003e \u003cp\u003e4.6.3 Black’s Formulas and Implied Volatility.\u003c\/p\u003e \u003cp\u003eAppendix: Solution of the PDIE.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 IntensityLévy Models.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Intensity Models for Credit Risk.\u003c\/p\u003e \u003cp\u003e5.1.1 Jarrow–Turnbull Model.\u003c\/p\u003e \u003cp\u003e5.1.2 Cox Models.\u003c\/p\u003e \u003cp\u003e5.2 The Intensity-OU Model.\u003c\/p\u003e \u003cp\u003e5.3 Calibration of the Model on CDS Term Structures.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III: MULTIVARIATE MODELLING.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6 Multivariate Credit Products.\u003c\/p\u003e \u003cp\u003e6.1 CDOs.\u003c\/p\u003e \u003cp\u003e6.2 Credit Indices.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Collateralized Debt Obligations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction.\u003c\/p\u003e \u003cp\u003e7.2 The Gaussian One-Factor Model.\u003c\/p\u003e \u003cp\u003e7.3 Generic One-Factor Lévy Model.\u003c\/p\u003e \u003cp\u003e7.4 Examples of Lévy Models.\u003c\/p\u003e \u003cp\u003e7.5 Lévy Base Correlation.\u003c\/p\u003e \u003cp\u003e7.5.1 The Concept of Base Correlation.\u003c\/p\u003e \u003cp\u003e7.5.2 Pricing Non-Standard Tranches.\u003c\/p\u003e \u003cp\u003e7.5.3 Correlation Mapping for Bespoke CDOs.\u003c\/p\u003e \u003cp\u003e7.6 Delta-Hedging CDO tranches.\u003c\/p\u003e \u003cp\u003e7.6.1 Hedging with the CDS Index.\u003c\/p\u003e \u003cp\u003e7.6.2 Delta-Hedging with a Single-Name CDS.\u003c\/p\u003e \u003cp\u003e7.6.3 Mezz-Equity hedging.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Multivariate Index Modelling.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Black’s Model.\u003c\/p\u003e \u003cp\u003e8.2 VG Credit Spread Model.\u003c\/p\u003e \u003cp\u003e8.3 Pricing Swaptions using FFT.\u003c\/p\u003e \u003cp\u003e8.4 Multivariate VG Model.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART IV: EXOTIC STRUCTURED CREDIT RISK PRODUCTS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9 Credit CPPIs and CPDOs.\u003c\/p\u003e \u003cp\u003e9.1 Introduction.\u003c\/p\u003e \u003cp\u003e9.2 CPPIs.\u003c\/p\u003e \u003cp\u003e9.3 Gap Risk.\u003c\/p\u003e \u003cp\u003e9.4 CPDOs.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Asset-Backed Securities.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction.\u003c\/p\u003e \u003cp\u003e10.2 Default Models.\u003c\/p\u003e \u003cp\u003e10.2.1 Generalized Logistic Default Model.\u003c\/p\u003e \u003cp\u003e10.2.2 Lévy Portfolio Default Model.\u003c\/p\u003e \u003cp\u003e10.2.3 Normal One-Factor Default Model.\u003c\/p\u003e \u003cp\u003e10.2.4 Generic One-Factor Lévy Default Model.\u003c\/p\u003e \u003cp\u003e10.3 Prepayment Models.\u003c\/p\u003e \u003cp\u003e10.3.1 Constant Prepayment Model.\u003c\/p\u003e \u003cp\u003e10.3.2 Lévy Portfolio Prepayment Model.\u003c\/p\u003e \u003cp\u003e10.3.3 Normal One-Factor Prepayment Model.\u003c\/p\u003e \u003cp\u003e10.4 Numerical Results.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBibliography.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402422985047,"sku":"9780470743065","price":110.42,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470743065.jpg?v=1730480353"},{"product_id":"probability-statistics-and-stochastic-processes-9780470889749","title":"Probability Statistics and Stochastic Processes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e. . . an excellent textbook . . . well organized and neatly written.\u003cbr\u003e \u003cb\u003e\u003ci\u003eMathematical Reviews\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e. . . amazingly interesting . . .\u003cbr\u003e \u003cb\u003e\u003ci\u003eTechnometrics\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, \u003ci\u003eProbability, Statistics, and Stochastic Processes\u003c\/i\u003e, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields.\u003c\/p\u003e \u003cp\u003eBeginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers'' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on stati\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003ePreface xi\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePreface to the First Edition xiii\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Basic Probability Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Sample Spaces and Events 3\u003c\/p\u003e \u003cp\u003e1.3 The Axioms of Probability 7\u003c\/p\u003e \u003cp\u003e1.4 Finite Sample Spaces and Combinatorics 15\u003c\/p\u003e \u003cp\u003e1.4.1 Combinatorics 17\u003c\/p\u003e \u003cp\u003e1.5 Conditional Probability and Independence 27\u003c\/p\u003e \u003cp\u003e1.6 The Law of Total Probability and Bayes’ Formula 41\u003c\/p\u003e \u003cp\u003eProblems 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Random Variables 76\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 76\u003c\/p\u003e \u003cp\u003e2.2 Discrete Random Variables 77\u003c\/p\u003e \u003cp\u003e2.3 Continuous Random Variables 82\u003c\/p\u003e \u003cp\u003e2.4 Expected Value and Variance 95\u003c\/p\u003e \u003cp\u003e2.5 Special Discrete Distributions 111\u003c\/p\u003e \u003cp\u003e2.6 The Exponential Distribution 123\u003c\/p\u003e \u003cp\u003e2.7 The Normal Distribution 127\u003c\/p\u003e \u003cp\u003e2.8 Other Distributions 131\u003c\/p\u003e \u003cp\u003e2.9 Location Parameters 137\u003c\/p\u003e \u003cp\u003e2.10 The Failure Rate Function 139\u003c\/p\u003e \u003cp\u003eProblems 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Joint Distributions 156\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 156\u003c\/p\u003e \u003cp\u003e3.2 The Joint Distribution Function 156\u003c\/p\u003e \u003cp\u003e3.3 Discrete Random Vectors 158\u003c\/p\u003e \u003cp\u003e3.4 Jointly Continuous Random Vectors 160\u003c\/p\u003e \u003cp\u003e3.5 Conditional Distributions and Independence 164\u003c\/p\u003e \u003cp\u003e3.5.1 Independent Random Variables 168\u003c\/p\u003e \u003cp\u003e3.6 Functions of Random Vectors 172\u003c\/p\u003e \u003cp\u003e3.7 Conditional Expectation 185\u003c\/p\u003e \u003cp\u003e3.8 Covariance and Correlation 196\u003c\/p\u003e \u003cp\u003e3.9 The Bivariate Normal Distribution 209\u003c\/p\u003e \u003cp\u003e3.10 Multidimensional Random Vectors 216\u003c\/p\u003e \u003cp\u003e3.11 Generating Functions 231\u003c\/p\u003e \u003cp\u003e3.12 The Poisson Process 240\u003c\/p\u003e \u003cp\u003eProblems 247\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Limit Theorems 263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 263\u003c\/p\u003e \u003cp\u003e4.2 The Law of Large Numbers 264\u003c\/p\u003e \u003cp\u003e4.3 The Central Limit Theorem 268\u003c\/p\u003e \u003cp\u003e4.4 Convergence in Distribution 275\u003c\/p\u003e \u003cp\u003eProblems 278\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Simulation 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 281\u003c\/p\u003e \u003cp\u003e5.2 Random Number Generation 282\u003c\/p\u003e \u003cp\u003e5.3 Simulation of Discrete Distributions 283\u003c\/p\u003e \u003cp\u003e5.4 Simulation of Continuous Distributions 285\u003c\/p\u003e \u003cp\u003e5.5 Miscellaneous 290\u003c\/p\u003e \u003cp\u003eProblems 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Statistical Inference 294\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 294\u003c\/p\u003e \u003cp\u003e6.2 Point Estimators 294\u003c\/p\u003e \u003cp\u003e6.3 Confidence Intervals 304\u003c\/p\u003e \u003cp\u003e6.4 Estimation Methods 312\u003c\/p\u003e \u003cp\u003e6.5 Hypothesis Testing 327\u003c\/p\u003e \u003cp\u003e6.6 Further Topics in Hypothesis Testing 334\u003c\/p\u003e \u003cp\u003e6.7 Goodness of Fit 339\u003c\/p\u003e \u003cp\u003e6.8 Bayesian Statistics 351\u003c\/p\u003e \u003cp\u003e6.9 Nonparametric Methods 363\u003c\/p\u003e \u003cp\u003eProblems 378\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Linear Models 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 391\u003c\/p\u003e \u003cp\u003e7.2 Sampling Distributions 392\u003c\/p\u003e \u003cp\u003e7.3 Single Sample Inference 395\u003c\/p\u003e \u003cp\u003e7.4 Comparing Two Samples 402\u003c\/p\u003e \u003cp\u003e7.5 Analysis of Variance 409\u003c\/p\u003e \u003cp\u003e7.6 Linear Regression 415\u003c\/p\u003e \u003cp\u003e7.7 The General Linear Model 431\u003c\/p\u003e \u003cp\u003eProblems 436\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Stochastic Processes 444\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 444\u003c\/p\u003e \u003cp\u003e8.2 Discrete -Time Markov Chains 445\u003c\/p\u003e \u003cp\u003e8.3 Random Walks and Branching Processes 464\u003c\/p\u003e \u003cp\u003e8.4 Continuous -Time Markov Chains 475\u003c\/p\u003e \u003cp\u003e8.5 Martingales 494\u003c\/p\u003e \u003cp\u003e8.6 Renewal Processes 502\u003c\/p\u003e \u003cp\u003e8.7 Brownian Motion 509\u003c\/p\u003e \u003cp\u003eProblems 517\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Tables 527\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Answers to Selected Problems 535\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFurther Reading 551\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 553\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402452705623,"sku":"9780470889749","price":102.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470889749.jpg?v=1730480442"},{"product_id":"operational-subjective-statistical-methods-9780471143291","title":"Operational Subjective Statistical Methods","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMethods of subjective statistical analysis have seen a resurgence of activity in the last decade. This book treats the theory of probability and the logic of uncertainty in a systematic way. It features a technical presentation of the mathematical impact of personal beliefs and values on statistical analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...has a merit for everyone who wonders about the foundations ofinference...\" (Australian \u0026amp; New Zealand J Statistics, 2000)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePhilosophical and Historical Introduction.\u003cbr\u003e \u003cbr\u003e Quantities, Prevision, and Coherency.\u003cbr\u003e \u003cbr\u003e Coherent Statistical Inference.\u003cbr\u003e \u003cbr\u003e Related Forms for Asserting Uncertain Knowledge.\u003cbr\u003e \u003cbr\u003e Distribution Functions.\u003cbr\u003e \u003cbr\u003e Proper Scoring Rules.\u003cbr\u003e \u003cbr\u003e The Multivariate Normal Distribution and Its Mixtures.\u003cbr\u003e \u003cbr\u003e Sequential Forecasting Based on Linear Conditional PrevisionStructures: Theory and Practice of Linear Regression.\u003cbr\u003e \u003cbr\u003e The Direction of Statistical Research.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402497368407,"sku":"9780471143291","price":157.45,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471143291.jpg?v=1730480589"},{"product_id":"statistical-methods-in-analytical-chemistry-9780471293637","title":"Statistical Methods in Analytical Chemistry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis edition continues to provide analytical chemists and statisticians with the latest practical information on using statistical tools in chemical data analysis. The accompanying FTP site contains a series of programs that illustrate the statistical techniques which are discussed in the book.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This new edition of a successful, bestselling book continues to provide you with practical information on the use\u003cbr\u003eof statistical methods for solving real-world problems in complex industrial environments.”  (PDFCHM Online, 27 February 2013)\u003c\/p\u003e \"...a comprehensive, very useful and clear guide for all analytical chemists...\" (Annali di Chimica, Vol 153, 2000)\u003cbr\u003e \u003cbr\u003e \"Substantially updated...for lab supervisors and project mangers, and is useful...for advanced students of chemistry and pharmaceutical science.\" (SciTech Book News, Vol. 24, No. 2, June 2001)\u003cbr\u003e \u003cbr\u003e \"Its clarity, focus and logical approach to statistical analysis of chemical data make it a book that should appear on the bookshelf of most analytical chemists.\" (Journal of the American Chemical Society, Vol. 123 No. 36)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eUnivariate Data.\u003cbr\u003e \u003cbr\u003e Bi- and Multivariate Data.\u003cbr\u003e \u003cbr\u003e Related Topics.\u003cbr\u003e \u003cbr\u003e Complex Examples.\u003cbr\u003e \u003cbr\u003e Appendices.\u003cbr\u003e \u003cbr\u003e Technical Tidbits.\u003cbr\u003e \u003cbr\u003e Glossary.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402555269463,"sku":"9780471293637","price":175.46,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471293637.jpg?v=1730480744"},{"product_id":"numerical-methods-for-stochastic-processes-9780471546412","title":"Numerical Methods for Stochastic Processes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis study deals with the calculations of mathematical expectations, primarily by simulation methods. The authors explore the present state of research and signal the types of problems raised by new methods. Topics discussed include Monte Carlo methods and the simulation of stochastic processes.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreliminaries.\u003cbr\u003e \u003cbr\u003e Computation of Expectations in Finite Dimension.\u003cbr\u003e \u003cbr\u003e Simulation of Random Processes.\u003cbr\u003e \u003cbr\u003e Deterministic Resolution of Some Markovian Problems.\u003cbr\u003e \u003cbr\u003e Stochastic Differential Equations and Brownian Functionals.\u003cbr\u003e \u003cbr\u003e Notes.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402628505943,"sku":"9780471546412","price":184.46,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471546412.jpg?v=1730481034"},{"product_id":"markov-processes-9780471769866","title":"Markov Processes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.\u003cbr\u003e \u003cbr\u003e [A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference.\u003cbr\u003e -American Scientist\u003cbr\u003e \u003cbr\u003e There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings.\u003cbr\u003e -Zentralblatt für Mathematik und ihre Grenzgebiete\/Mathematics Abstracts\u003cbr\u003e \u003cbr\u003e Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference w\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.  \u003cp\u003e1. Operator Semigroups.\u003c\/p\u003e \u003cp\u003e2. Stochastic Processes and Martingales.\u003c\/p\u003e \u003cp\u003e3. Convergence of Probability Measures.\u003c\/p\u003e \u003cp\u003e4. Generators and Markov Processes.\u003c\/p\u003e \u003cp\u003e5. Stochastic Integral Equations.\u003c\/p\u003e \u003cp\u003e6. Random Time Changes.\u003c\/p\u003e \u003cp\u003e7. Invariance Principles and Diffusion Approximations.\u003c\/p\u003e \u003cp\u003e8. Examples of Generators.\u003c\/p\u003e \u003cp\u003e9. Branching Processes.\u003c\/p\u003e \u003cp\u003e10. Genetic Models.\u003c\/p\u003e \u003cp\u003e11. Density Dependent Population Processes.\u003c\/p\u003e \u003cp\u003e12. Random Evolutions.\u003c\/p\u003e \u003cp\u003eAppendixes.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e \u003cp\u003eFlowchart.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402671006039,"sku":"9780471769866","price":107.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471769866.jpg?v=1730481179"},{"product_id":"counting-processes-and-survival-analysis-9780471769880","title":"Counting Processes and Survival Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book explores the martingale approach to the statistical analysis of counting processes, with an emphasis on application of those methods to censored failure time data. Introduced in the 1970s, this approach has proven to be remarkably successful in yielding results about statistical methods for many problems arising in censored data.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"…a unique source for combining the theory and the application of the survival analysis with censored data.\" (\u003ci\u003eTechnometrics\u003c\/i\u003e, August 2007)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003e0. The Applied Setting.\u003c\/p\u003e \u003cp\u003e1. The Counting Process and Martingale Framework.\u003c\/p\u003e \u003cp\u003e2. Local Square Integrable Martingales.\u003c\/p\u003e \u003cp\u003e3. Finite Sample Moments and Large Sample Consistency of Tests and Estimators.\u003c\/p\u003e \u003cp\u003e4. Censored Data Regression Models and Their Application.\u003c\/p\u003e \u003cp\u003e5. Martingale Central Limit Theorem.\u003c\/p\u003e \u003cp\u003e6. Large Sample results of the Kaplan-Meier Estimator.\u003c\/p\u003e \u003cp\u003e7. Weighted Logrank Statistics.\u003c\/p\u003e \u003cp\u003e8. Distribution Theory for Proportional Hazards Regression.\u003c\/p\u003e \u003cp\u003eAppendix A: Some Results from stieltjes Integration and Probability Theory.\u003c\/p\u003e \u003cp\u003eAppendix B: An Introduction to Weak convergence.\u003c\/p\u003e \u003cp\u003eAppendix C: The Martingale Central Limit Theorem: Some Preliminaries.\u003c\/p\u003e \u003cp\u003eAppendix D: Data.\u003c\/p\u003e \u003cp\u003eAppendix E: Exercises.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eNotation.\u003c\/p\u003e \u003cp\u003eAuthor Index.\u003c\/p\u003e \u003cp\u003eSubject Index.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402671104343,"sku":"9780471769880","price":101.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471769880.jpg?v=1730481179"},{"product_id":"practical-statistics-for-experimental-biologists-9780471988229","title":"Practical Statistics for Experimental Biologists","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA good working knowledge of statistical principles is needed for both the design and analysis of biological experiments and the subsequent handling of the large amounts of data generated if worthwhile, reliable conclusions are to be reached.\u003cbr\u003e Practical Statistics for Experimental Biologists, Second Edition provides biologists with a user-friendly, non-technical introduction to the basics of statistics. The book has been thoroughly revised and updated to incorporate:\u003cbr\u003e * Worked examples and printouts from MINITAB\u003cbr\u003e * Relevant case studies and applications\u003cbr\u003e * Further Notes section for background explanations\u003cbr\u003e Written by a biologist with extensive experience of applying statistical procedures to experimental systems, this book will be invaluable to undergraduates, postgraduates and researchers in microbiology, immunology, biochemistry, botany, zoology, physiology, pharmacology and pharmacy.\u003cbr\u003e Review of the First Edition\u003cbr\u003e ...strongly recommended as the current first choic\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...a refreshing and useful book...\" ---- Trends in Plant Science, September 2000\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA Simple Experiment in Pipetting.\u003cbr\u003e \u003cbr\u003e How to Condense the Bulkiness of Data.\u003cbr\u003e \u003cbr\u003e Are Those Differences Significant?\u003cbr\u003e \u003cbr\u003e More About Measurement Differences.\u003cbr\u003e \u003cbr\u003e Awkward-Measurement Data.\u003cbr\u003e \u003cbr\u003e How to Deal with Count Data.\u003cbr\u003e \u003cbr\u003e How to Deal with Proportion Data.\u003cbr\u003e \u003cbr\u003e Correlation and Regression.\u003cbr\u003e \u003cbr\u003e Dose-Response Lines and Assays.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Additional Reading.\u003cbr\u003e \u003cbr\u003e Appendices.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402710491479,"sku":"9780471988229","price":62.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471988229.jpg?v=1730481303"},{"product_id":"randomness-9780674107465","title":"Randomness","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eClearly, the computation of probabilities is not just an arid game… As Deborah Bennett shows in her excellent little book on the mathematics of chance, the concept has been controversial for thousands of years… [Her] cultured and accessible book goes a long way towards demystifying the science of probability and thereby offers the reader a useful variety of conceptual tools with which to probe the future and illuminate the present. -- Steven Poole * The Guardian *\u003cbr\u003e[\u003ci\u003eRandomness\u003c\/i\u003e] can most easily be described as a brief history of chance… I can cheerfully recommend it to anyone who is a total beginner when it comes to probability, what it means, why it is desperately puzzling, and what it can do for us despite that… It is fascinating to read about the pioneers of probability, such as Pierre Simon de Laplace with his ‘normal distribution’—now more familiar as the notorious bell curve—and Adolphe Quetelet, perhaps the first to realise that there are statistical patterns in human behaviour. And I applaud the blunt reminder that when it comes to the real world the ‘normal’ distribution is actually highly abnormal… My main criticism: it left me wanting more. A sequel, please. -- Ian Stewart * Times Higher Education Supplement *\u003cbr\u003eChances are high that reading this book will clear up your misconceptions about randomness and probabilities. In this very entertaining little book, simply written but intended for careful readers, some of the most common mistakes people make about chance are carefully analyzed. While describing interesting aspects of the mathematics of probability, the author takes frequent detours into the history of humanity’s understanding (and misunderstanding) of the laws of chance, touching on subjects as diverse as chance in decision-making and the fairness of those decisions, gambling and our intuitive understanding of chance, the likelihood of the extremely rare, the existence of true randomness and how computers have helped shape modern thinking about probabilities… An insightful chapter is ‘Chance or Necessity?’ The question is very, very old (determinism versus chaos), and the answer is not clear even today. The author describes the problem beautifully: ‘Is random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors?’ Einstein grappled with this conundrum until his death and never ceased to combat the idea that God could conceivably throw dice… Whether well-educated in mathematics or not, people have always been fascinated by randomness and intrigued by the fundamental question of the real nature of randomness, of how you can tell randomness from something that is not. -- J. A. Rial * American Scientist *\u003cbr\u003eThe great strength of this book is the way it uses history and even prehistory of probability to chart its present territory and cast light on its core point of contention: does true randomness exist in nature, or is it only a psychological artefact?… Bennett’s text…is like a café conversation between likable cognoscenti…nothing could more provoke and excite the reader. -- Simon Ings * New Scientist *\u003cbr\u003eIn this book, Bennett seeks to account for the centuries-long lapse between early uses of chance in decision making and the more technical studies of probability first undertaken in the seventeenth century. At the same time, she explores the confusions and misunderstandings about probability that persist today. She argues that the notion of randomness played a crucial role in inhibiting conceptual progress in probability and that it also accounts for present-day struggles to come to terms with the subject… Bennett’s book is written in a lucid, engaging style and provides an entertaining introduction to some questions in probability. -- Patti Wilger Hunter * Isis *\u003cbr\u003e[A] sharp analysis of the way we assess probability in everyday life. -- Robert Winder * New Statesman \u0026amp; Society *\u003cbr\u003e\u003ci\u003eRandomness\u003c\/i\u003e, by mathematician Deborah J. Bennett, was obviously a labor of love. The result is an interesting book that combines a well-researched, anecdotally presented survey of the history of chance, probability and randomness along with some elementary instruction in probability… It includes a wide-ranging and rich bibliography that reflects the passion of the author for the subject. Anybody interested in gaming, random numbers, the Monte Carlo method and so on will find nice anecdotal descriptions of these topics, together with detailed notes and references to the bibliography for more detailed study. It is a good book to have. -- Stephen Gasiorowicz * Physics Today *\u003cbr\u003eIn 1996 Charles Hailey and David Helfand reported their calculations of the odds of a commercial airliner being struck by a meteor, in response to speculation about TWA flight 800… They conclude that, in over 30 years of air travel, the probability that a commercial flight would have been hit by a meteor big enough to crash it is 1 in 10. This bit of probability trivia is an indication of human beings continuous struggle to understand probability and chance through the ages, and Deborah Bennett captures the fascination with numbers in this pocket-sized volume. The book is filled with…gems. * Skeptic *\u003cbr\u003eThis volume is exceptionally readable. It takes away much of the mystery of probability while adding to our sense of wonder. * Wordtrade *\u003cbr\u003eThe fact that randomness, agency, and holiness can readily displace each other in phenomenological explanations of human action is the central concern that might draw students of consciousness to Bennett’s book. Bennett does an excellent job, explaining and drawing out the major questions that swirl around the randomness–agency–holiness issue. -- T. W. Draper * Journal of Consciousness Studies *\u003cbr\u003e[This book] examines randomness and several other notions that were critical to the historical development of probabilistic thinking and that also play an important role in any individual’s understanding of the laws of chance. [It] addresses why, from ancient times to today, people have resorted to chance in making decisions; whether a decision made by random choice is a fair decision; how to figure the odds; what role gambling has played in understanding chance; whether extremely rare events are likely in the long run; why some societies and individuals reject randomness; whether true randomness exists; the view of randomness as uncertainty; why even experts disagree about the many meanings of randomness; and why probability is so counterintuitive. * Journal of Economic Literature *\u003cbr\u003eMathematics is its own language, and sometimes it doesn’t translate readily into other human tongues. But Bennett is brilliantly bilingual, well able to put mathematical concepts into clear, expressive English. Her topic is intrinsically fascinating, for who has not felt buffeted by random events, and who has not sought to see when the wheel of fortune may turn up good luck?… More than an intriguing exploration of a peculiarly fascinating part of mathematics, its coverage, ranging from ancient games of chance to modern probability mind-games, makes it comprehensive as well as compulsively readable. -- Patricia Monaghan * Booklist *\u003cbr\u003eA clear and detailed examination of the role of pure chance, with fascinating historical asides. * Kirkus Reviews *\u003cbr\u003eA careful and well-written treatment of an intriguing subject. -- Donald Goldsmith, author of \u003ci\u003eThe Ultimate Einstein\u003c\/i\u003e\u003cbr\u003e\u003ci\u003eRandomness\u003c\/i\u003e tells us about chance by recalling the real history of probability and solving many of its engaging puzzles. Beginners will find themselves welcomed and well led. -- Frederick Mosteller, Harvard University\u003cbr\u003eRandomness explains probability and odds in an accessible way. This book puts risk and chance into perspective for the airline passenger and the lottery player alike. -- Henry Petroski, author of \u003ci\u003eInvention by Design: How Engineers Get from Thought to Thing\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* Chance Encounters \t* Why Resort to Chance? \t* When the Gods Played Dice \t* Figuring the Odds \t* Thought Games for Gamblers \t* Chance or Necessity? \t* Order in Apparent Chaos \t* Wanted: Random Numbers \t* Randomness as Uncertainty \t* Paradoxes in Probability  \t* Notes \t* Bibliography \t* Index","brand":"Harvard University Press","offers":[{"title":"Default Title","offer_id":49403557347671,"sku":"9780674107465","price":24.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780674107465.jpg?v=1730483824"},{"product_id":"quantal-response-equilibrium-a-stochastic-theory-of-games-9780691124230","title":"Quantal Response Equilibrium  A Stochastic Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eQuantal Response Equilibrium presents a stochastic theory of games that unites probabilistic choice models developed in psychology and statistics with the Nash equilibrium approach of classical game theory. Nash equilibrium assumes precise and perfect decision making in games, but human behavior is inherently stochastic and people realize that the\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book brings together two decades of scholarship on an important model of boundedly rational behavior in strategic decision-making settings. Including numerous important applications in economics, political science, and pure game theory, this unified treatment will be valuable to a wide range of scholars.\"\u003cb\u003e—Timothy Cason, Purdue University\u003c\/b\u003e\u003cbr\u003e\"Quantal response equilibrium is a standard tool for game theorists and has numerous connections to other tools and applications. This book collects and extends existing material on QRE and is a significant contribution to pure, and especially applied, game theory. No other books explicate QRE systematically beyond the introductory level and these authors are the right team for pulling the core material together.\"\u003cb\u003e—Daniel Friedman, University of California, Santa Cruz\u003c\/b\u003e\u003cbr\u003e\"Well-written and easy to follow, this book covers the topic of quantal response equilibrium. The notion of stochastic equilibrium has changed the way game theorists think about long-run and short-run equilibrium. Written by three leading experts, this book is of great importance to researchers in economic theory and political science, and to graduate students.\"\u003cb\u003e—David K. Levine, European University Institute\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. v*Preface, pg. ix*1. Introduction and Background, pg. 1*2. Quantal Response Equilibrium in Normal-Form Games, pg. 10*3. Quantal Response Equilibrium in Extensive-Form Games, pg. 63*4. Heterogeneity, pg. 88*5. Dynamics and Learning, pg. 112*6. QRE as a Structural Model for Estimation, pg. 141*7. Applications to Game Theory, pg. 161*8. Applications to Political Science, pg. 206*9. Applications to Economics, pg. 248*10. Epilogue: Some Thoughts about Future Research, pg. 281*References, pg. 291*Index, pg. 301","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403740029271,"sku":"9780691124230","price":52.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691124230.jpg?v=1730484409"},{"product_id":"nonlinear-dynamical-systems-and-control-9780691133294","title":"Nonlinear Dynamical Systems and Control","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. This graduate-level textbook is suitable for applied mathematicians, dynamical systems theorists, control theorists, and engineers.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eWassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics \"The book is lucid and well written and contains numerous worked examples for specific applications to important classes of systems as well as numerous problems and suggestions for further study at the end of the main chapters. This book will be an excellent source of reference materials for graduate students of applied mathematics, control theorists and engineers studying the stability theory of dynamical systems and controls. It will also be a rich source of materials for self study by researchers and practitioners interested in systems theory of engineering, controls, computer science, chemistry, life sciences and economics.\"--Olusola Akinyele, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eConventions and Notation xv  Preface xxi  Chapter 1. Introduction 1  Chapter 2. Dynamical Systems and Differential Equations 9  Chapter 3. Stability Theory for Nonlinear Dynamical Systems 135  Chapter 4. Advanced Stability Theory 207  Chapter 5. Dissipativity Theory for Nonlinear Dynamical Systems 325  Chapter 6. Stability and Optimality of Feedback Dynamical Systems 411  Chapter 7. Input-Output Stability and Dissipativity 471  Chapter 8. Optimal Nonlinear Feedback Control 511  Chapter 9. Inverse Optimal Control and Integrator Backstepping 557  Chapter 10. Disturbance Rejection Control for Nonlinear Dynamical Systems 603  Chapter 11. Robust Control for Nonlinear Uncertain Systems 649  Chapter 12. Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions 719  Chapter 13. Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems 763  Chapter 14. Discrete-Time Optimal Nonlinear Feedback Control 845  Bibliography 901  Index 939","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403752710487,"sku":"9780691133294","price":120.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691133294.jpg?v=1730484443"},{"product_id":"mathematical-analysis-of-deterministic-and-stochastic-problems-in-complex-media-electromagnetics-9780691142173","title":"Mathematical Analysis of Deterministic and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eElectromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. This book introduces the electromagnetics of complex media through a systematic account of their mathematical theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems.\"--Vilmos Komornik, Mathematical Reviews\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi       PART 1. MODELLING AND MATHEMATICAL PRELIMINARIES 1       Chapter 1. Complex Media 3   Chapter 2. The Maxwell Equations and Constitutive Relations 9   2.1 Introduction 9   2.2 Fundamentals 9   2.3 Constitutive relations 13   2.4 The Maxwell equations in complex media: A variety of problems 23       Chapter 3. Spaces and Operators 38   3.1 Introduction 38   3.2 Function spaces 38   3.3 Standard difierential and trace operators 45   3.4 Function spaces for electromagnetics 48   3.5 Traces 51   3.6 Various decompositions 52   3.7 Compact embeddings 53   3.8 The operators of vector analysis revisited 54   3.9 The Maxwell operator 56       PART 2. TIME-HARMONIC DETERMINISTIC PROBLEMS 59       Chapter 4. Well Posedness 61   4.1 Introduction 61   4.2 Solvability of the interior problem 62   4.3 The eigenvalue problem 68   4.4 Low chirality behaviour 70   4.5 Comments on exterior domain problems 74   4.6 Towards numerics 77       Chapter 5. Scattering Problems: Beltrami Fields and Solvability 83   5.1 Introduction 83   5.2 Elliptic, circular and linear polarisation of waves 84   5.3 Beltrami fields - The Bohren decomposition 86   5.4 Scattering problems: Formulation 88   5.5 An introduction to BIEs 91   5.6 Properties of Beltrami fields 96   5.7 Solvability 99   5.8 Generalised Muller's BIEs 106   5.9 Low chirality approximations 108   5.10 Miscellanea 109       Chapter 6. Scattering Problems: A Variety of Topics 112   6.1 Introduction 112   6.2 Important concepts of scattering theory 113   6.3 Back to chiral media: Scattering relations and the far-field operator 118   6.4 Using dyadics 124   6.5 Herglotz wave functions 129   6.6 Domain derivative 136   6.7 Miscellanea 140       PART 3. TIME-DEPENDENT DETERMINISTIC PROBLEMS 149       Chapter 7. Well Posedness 151   7.1 Introduction 151   7.2 The Maxwell equations in the time domain 151   7.3 Functional framework and assumptions 152   7.4 Solvability 153   7.5 Other possible approaches to solvability 158   7.6 Miscellanea 162       Chapter 8. Controllability 163   8.1 Introduction 163   8.2 Formulation 163   8.3 Controllability of achiral media: The Hilbert Uniqueness method 165   8.4 The forward and backward problems 167   8.5 Controllability: Complex media 174   8.6 Miscellanea 176       Chapter 9. Homogenisation 180   9.1 Introduction 180   9.2 Formulation 181   9.3 A formal two-scale expansion 184   9.4 The optical response region 188   9.5 General bianisotropic media 199   9.6 Miscellanea 207       Chapter 10. Towards a Scattering Theory 212   10.1 Introduction 212   10.2 Formulation 213   10.3 Some basic strategies 214   10.4 On the construction of solutions 217   10.5 Wave operators and their construction 220   10.6 Complex media electromagnetics 225   10.7 Miscellanea 229       Chapter 11. Nonlinear Problems 231   11.1 Introduction 231   11.2 Formulation 231   11.3 Well posedness of the model 232   11.4 Miscellanea 241       PART 4. STOCHASTIC PROBLEMS 245       Chapter 12. Well Posedness 247   12.1 Introduction 247   12.2 Maxwell equations for random media 248   12.3 Functional setting 249   12.4 Well posedness 250   12.5 Other possible approaches to solvability 255   12.6 Miscellanea 261      Chapter 13. Controllability 263   13.1 Introduction 263   13.2 Formulation 263   13.3 Subtleties of stochastic controllability 264   13.4 Approximate controllability I: Random PDEs 266   13.5 Approximate controllability II: BSPDEs 269   13.6 Miscellanea 272       Chapter 14. Homogenisation 275   14.1 Introduction 275   14.2 Ergodic media 276   14.3 Formulation 279   14.4 A formal two-scale expansion 282   14.5 Homogenisation of the Maxwell system 284   14.6 Miscellanea 288       PART 5. APPENDICES 291       Appendix A. Some Facts from Functional Analysis 293   A.1 Duality 293   A.2 Strong, weak and weak-* convergence 295   A.3 Calculus in Banach spaces 297   A.4 Basic elements of spectral theory 300   A.5 Compactness criteria 303   A.6 Compact operators 304   A.7 The Banach-Steinhaus theorem 308   A.8 Semigroups and the Cauchy problem 308   A.9 Some fixed point theorems 312   A.10 The Lax-Milgram lemma 313   A.11 Gronwall's inequality 314   A.12 Nonlinear operators 315       Appendix B. Some Facts from Stochastic Analysis 316   B.1 Probability in Hilbert spaces 316   B.2 Stochastic processes and random fields 318   B.3 Gaussian measures 319   B.4 The Q- and the cylindrical Wiener process 320   B.5 The Ito integral 321   B.6 Ito formula 324   B.7 Stochastic convolution 325   B.8 SDEs in Hilbert spaces 325   B.9 Martingale representation theorem 326       Appendix C. Some Facts from Elliptic Homogenisation Theory 327   C.1 Spaces of periodic functions 327   C.2 Compensated compactness 329   C.3 Homogenisation of elliptic equations 329   C.4 Random elliptic homogenisation theory 332   Appendix D. Some Facts from Dyadic Analysis (by George Dassios) 334   Appendix E. Notation and abbreviations 341       Bibliography 343   Index 377","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403768930647,"sku":"9780691142173","price":106.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691142173.jpg?v=1730484487"},{"product_id":"handbook-of-stochastic-analysis-and-applications-9780824706609","title":"Handbook of Stochastic Analysis and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eMarkov processes and their applications; semimartingale theory and stochastic calculus; white noise theory; stochastic differential equations and its applications; large deviations and applications; a brief introduction to numerical analysis of (ordinary) stochastic differential equations without tears; stochastic differential games and applications; stability and stabilizing control of stochastic systems; stochastic approximation - theory and applications; stochastic manufacturing systems; optimization by stochastic methods; stochastic control methods in asset pricing.","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49406174527831,"sku":"9780824706609","price":275.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780824706609.jpg?v=1730494787"},{"product_id":"game-theory-9781108493451","title":"Game Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eNow in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual for instructors with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful re\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003ePraise for first edition: 'This is the book for which the world has been waiting for decades: a definitive, comprehensive account of the mathematical theory of games, by three of the world's biggest experts on the subject. Rigorous yet eminently readable, deep yet comprehensible, replete with a large variety of important real-world applications, it will remain the standard reference in game theory for a very long time.' Robert Aumann, Nobel Laureate in Economics, The Hebrew University of Jerusalem\u003cbr\u003ePraise for first edition: 'Without any sacrifice on the depth or the clarity of the exposition, this book is amazing in its breadth of coverage of the important ideas of game theory. It covers classical game theory, including utility theory, equilibrium refinements and belief hierarchies; classical cooperative game theory, including the core, Shapley value, bargaining set and nucleolus; major applications, including social choice, auctions, matching and mechanism design; and the relevant mathematics of linear programming and fixed point theory. The comprehensive coverage combined with the depth and clarity of exposition makes it an ideal book not only to learn game theory from, but also to have on the shelves of working game theorists.' Ehud Kalai, Kellogg School of Management, Northwestern University\u003cbr\u003ePraise for first edition: 'The best and the most comprehensive textbook for advanced courses in game theory.' David Schmeidler, Ohio State University and Tel Aviv University\u003cbr\u003ePraise for first edition: 'There are quite a few good textbooks on game theory now, but for rigor and breadth this one stands out.' Eric S. Maskin, Nobel Laureate in Economics, Harvard University, Massachusetts\u003cbr\u003ePraise for first edition: 'This textbook provides an exceptionally clear and comprehensive introduction to both cooperative and noncooperative game theory. It deftly combines a rigorous exposition of the key mathematical results with a wealth of illuminating examples drawn from a wide range of subjects. It is a tour de force.' Peyton Young, University of Oxford\u003cbr\u003ePraise for first edition: 'This is a wonderful introduction to game theory, written in a way that allows it to serve both as a text for a course and as a reference … The book is written by leading figures in the field [whose] broad view of the field suffuses the material.' Joe Halpern, Cornell University, New York\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. The game of chess; 2. Utility theory; 3. Extensive-form games; 4. Strategic-form games; 5. Mixed strategies; 6. Behavior strategies and Kuhn's theorem; 7. Equilibrium refinements; 8. Correlated equilibria; 9. Games with incomplete information and common priors; 10. Games with incomplete information: the general model; 11. The universal belief space; 12. Auctions; 13. Repeated games; 14. Repeated games with vector payoffs; 15. Social choice; 16. Bargaining games; 17. Coalitional games with transferable utility; 18. The core; 19. The Shapley value; 20. The bargaining set; 21. The nucleolus; 22. Stable matching; 23. Appendices.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49406814388567,"sku":"9781108493451","price":118.75,"currency_code":"GBP","in_stock":true}]},{"product_id":"stochastic-structural-dynamics-application-of-finite-element-methods-9781118342350","title":"Stochastic Structural Dynamics Application of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOne of the first books to provide in-depth and systematic application of finite element methods to the field,   Stochastic Structural Dynamics presents and illustrates direct integration methods for analyzing the statistics of the response of structures to stochastic loads.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDedication xi\u003c\/p\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgements xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Displacement Formulation Based Finite Element Method 2\u003c\/p\u003e \u003cp\u003e1.2 Element Equations of Motion for Temporally and Spatially Stochastic Systems 13\u003c\/p\u003e \u003cp\u003e1.3 Hybrid Stress Based Element Equations of Motion 14\u003c\/p\u003e \u003cp\u003e1.4 Incremental Variational Principle and Mixed Formulation Based Nonlinear Element Matrices 18\u003c\/p\u003e \u003cp\u003e1.5 Constitutive Relations and Updating of Configurations and Stresses 36\u003c\/p\u003e \u003cp\u003e1.6 Concluding Remarks 48\u003c\/p\u003e \u003cp\u003eReferences 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Spectral Analysis and Response Statistics of Linear Structural Systems 53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Spectral Analysis 53\u003c\/p\u003e \u003cp\u003e2.2 Evolutionary Spectral Analysis 56\u003c\/p\u003e \u003cp\u003e2.3 Evolutionary Spectra of Engineering Structures 60\u003c\/p\u003e \u003cp\u003e2.4 Modal Analysis and Time-Dependent Response Statistics 76\u003c\/p\u003e \u003cp\u003e2.5 Response Statistics of Engineering Structures 79\u003c\/p\u003e \u003cp\u003eReferences 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Direct Integration Methods for Linear Structural Systems 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Stochastic Central Difference Method 97\u003c\/p\u003e \u003cp\u003e3.2 Stochastic Central Difference Method with Time Co-ordinate Transformation 100\u003c\/p\u003e \u003cp\u003e3.3 Applications 102\u003c\/p\u003e \u003cp\u003e3.4 Extended Stochastic Central Difference Method and Narrow-band Force Vector 114\u003c\/p\u003e \u003cp\u003e3.5 Stochastic Newmark Family of Algorithms 122\u003c\/p\u003e \u003cp\u003eReferences 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Modal Analysis and Response Statistics of Quasi-linear Structural Systems 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Modal Analysis of Temporally Stochastic Quasi-linear Systems 131\u003c\/p\u003e \u003cp\u003e4.2 Response Analysis Based on Melosh-Zienkiewicz-Cheung Bending Plate Finite Element 141\u003c\/p\u003e \u003cp\u003e4.3 Response Analysis Based on High Precision Triangular Plate Finite Element 156\u003c\/p\u003e \u003cp\u003e4.4 Concluding Remarks 166\u003c\/p\u003e \u003cp\u003eReferences 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Direct Integration Methods for Response Statistics of Quasi-linear Structural Systems 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Stochastic Central Difference Method for Quasi-linear Structural Systems 169\u003c\/p\u003e \u003cp\u003e5.2 Recursive Covariance Matrix of Displacements of Cantilever Pipe Containing Turbulent Fluid 174\u003c\/p\u003e \u003cp\u003e5.3 Quasi-linear Systems under Narrow-band Random Excitations 184\u003c\/p\u003e \u003cp\u003e5.4 Concluding Remarks 188\u003c\/p\u003e \u003cp\u003eReferences 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Direct Integration Methods for Temporally Stochastic Nonlinear Structural Systems 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Statistical Linearization Techniques 191\u003c\/p\u003e \u003cp\u003e6.2 Symplectic Algorithms of Newmark Family of Integration Schemes 194\u003c\/p\u003e \u003cp\u003e6.3 Stochastic Central Difference Method with Time Co-ordinate Transformation and Adaptive Time Schemes 199\u003c\/p\u003e \u003cp\u003e6.4 Outline of steps in computer program 211\u003c\/p\u003e \u003cp\u003e6.5 Large Deformations of Plate and Shell Structures 213\u003c\/p\u003e \u003cp\u003e6.6 Concluding Remarks 224\u003c\/p\u003e \u003cp\u003eReferences 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Direct Integration Methods for Temporally and Spatially Stochastic Nonlinear Structural Systems 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Perturbation Approximation Techniques and Stochastic Finite Element Methods 232\u003c\/p\u003e \u003cp\u003e7.2 Stochastic Central Difference Methods for Temporally and Spatially Stochastic Nonlinear Systems 241\u003c\/p\u003e \u003cp\u003e7.3 Finite Deformations of Spherical Shells with Large Spatially Stochastic Parameters 251\u003c\/p\u003e \u003cp\u003e7.4 Closing Remarks 255\u003c\/p\u003e \u003cp\u003eReferences 257\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1A Mass and Stiffness Matrices of Higher Order Tapered Beam Element 261\u003c\/p\u003e \u003cp\u003e1B Consistent Stiffness Matrix of Lower Order Triangular Shell Element 267\u003c\/p\u003e \u003cp\u003e1B.1 Inverse of Element Generalized Stiffness Matrix 267\u003c\/p\u003e \u003cp\u003e1B.2 Element Leverage Matrices 268\u003c\/p\u003e \u003cp\u003e1B.3 Element Component Stiffness Matrix Associated with Torsion 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 276\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1C Consistent Mass Matrix of Lower Order Triangular Shell Element 277\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReference 280\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2A Eigenvalue Solution 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 282\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2B Derivation of Evolutionary Spectral Densities and Variances of Displacements 283\u003c\/p\u003e \u003cp\u003e2B.1 Evolutionary Spectral Densities Due to Exponentially Decaying Random Excitations 283\u003c\/p\u003e \u003cp\u003e2B.2 Evolutionary Spectral Densities Due to Uniformly Modulated Random Excitations 286\u003c\/p\u003e \u003cp\u003e2B.3 Variances of Displacements 288\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2C Time-dependent Covariances of Displacements 299\u003c\/p\u003e \u003cp\u003e2D Covariances of Displacements and Velocities 311\u003c\/p\u003e \u003cp\u003e2E Time-dependent Covariances of Velocities 317\u003c\/p\u003e \u003cp\u003e2F Cylindrical Shell Element Matrices 323\u003c\/p\u003e \u003cp\u003e3A Deterministic Newmark Family of Algorithms 327\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReference 331\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 333\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406853415255,"sku":"9781118342350","price":91.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118342350.jpg?v=1730497347"}],"url":"https:\/\/bookcurl.com\/collections\/stochastics.oembed?page=8","provider":"Book Curl","version":"1.0","type":"link"}