Stochastics Books

Book SynopsisProbability 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 numbersTable of ContentsPART A BASIC PROBABILITY; PART B FURTHER PROBABILITY

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Book SynopsisThe fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, Arbitrage Theory in Continuous Time is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but with lots of intuitive economic arguments.In the substantially extended fourth edition Tomas Björk has added completely new chapters on incomplete markets, treating such topics as the Esscher trTrade ReviewReview from previous edition This book is one of the best of a large number of new books on mathematical and probabilistic models in finance, positioned between the books by Hull and Duffie on a mathematical scale...This is a highly reasonable book and strikes a balance between mathematical development and intuitive explanation. * Short Book Reviews *Table of Contents1: Introduction I. Discrete Time Models 2: The Binomial Model 3: A More General One period Model II. Stochastic Calculus 4: Stochastic Integrals 5: Stochastic Differential Equations III. Arbitrage Theory 6: Portfolio Dynamics 7: Arbitrage Pricing 8: Completeness and Hedging 9: A Primer on Incomplete Markets 10: Parity Relations and Delta Hedging 11: The Martingale Approach to Arbitrage Theory 12: The Mathematics of the Martingale Approach 13: Black-Scholes from a Martingale Point of View 14: Multidimensional Models: Martingale Approach 15: Change of Numeraire 16: Dividends 17: Forward and Futures Contracts 18: Currency Derivatives 19: Bonds and Interest Rates 20: Short Rate Models 21: Martingale Models for the Short Rate 22: Forward Rate Models 23: LIBOR Market Models 24: Potentials and Positive Interest IV. Optimal Control and Investment Theory 25: Stochastic Optimal Control 26: Optimal Consumption and Investment 27: The Martingale Approach to Optimal Investment 28: Optimal Stopping Theory and American Options V. Incomplete Markets 29: Incomplete Markets 30: The Esscher Transform and the Minimal Martingale Measure 31: Minimizing f-divergence 32: Portfolio Optimization in Incomplete Markets 33: Utility Indifference Pricing and Other Topics 34: Good Deal Bounds VI. Dynamic Equilibrium Theory 35: Equilibrium Theory: A Simple Production Model 36: The Cox-Ingersoll-Ross Factor Model 37: The Cox-Ingersoll-Ross Interest Rate Model 38: Endowment Equilibrium: Unit Net Supply

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Book SynopsisCompletely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance.Trade Review“As supplementary reading for a second course or as s comprehensive (!) resource for the general theory of processes aimed at Ph. D. students and scholars, this second edition will stay a valuable resource.” (René L. Schilling, Mathematical Reviews, October, 2016)“This is a fundamental book in modern stochastic calculus and its applications: rich contents, well structured material, comprehensive coverage of all significant results given with complete proofs and well illustrated by examples, carefully written text. Hence, there are more than enough reasons to strongly recommend the book to a wide audience. Among them, there are good and motivated graduate university students. … Also, the book is an excellent reference book.” (Jordan M. Stoyanov, zbMATH 1338.60001, 2016)Table of ContentsPart I: Measure Theoretic Probability.- Measure Integral.- Probabilities and Expectation.- Part II: Stochastic Processes.- Filtrations, Stopping Times and Stochastic Processes.- Martingales in Discrete Time.- Martingales in Continuous Time.- The Classification of Stopping Times.- The Progressive, Optional and Predicable -Algebras.- Part III: Stochastic Integration.- Processes of Finite Variation.- The Doob-Meyer Decomposition.- The Structure of Square Integrable Martingales.- Quadratic Variation and Semimartingales.- The Stochastic Integral.- Random Measures.- Part IV: Stochastic Differential Equations.- Ito's Differential Rule.- The Exponential Formula and Girsanov's Theorem.- Lipschitz Stochastic Differential Equations.- Markov Properties of SDEs.- Weak Solutions of SDEs.- Backward Stochastic Differential Equations.- Part V: Applications.- Control of a Single Jump.- Optimal Control of Drifts and Jump Rates.- Filtering. Part VI: Appendices.

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Book SynopsisTaken 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 departmeTrade ReviewWinner of the 2005 DeGroot Prize.From the reviews:"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." Technometrics, August 2004"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.'" Biometrics, December 2004"Although All of Statistics 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." The American Statistician, May 2005"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)"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)"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)"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)"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)Table of ContentsProbability.- 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.

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Book SynopsisNow 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 reTrade ReviewPraise 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 JerusalemPraise 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 UniversityPraise for first edition: 'The best and the most comprehensive textbook for advanced courses in game theory.' David Schmeidler, Ohio State University and Tel Aviv UniversityPraise 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, MassachusettsPraise 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 OxfordPraise 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 YorkTable of Contents1. 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.

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Book SynopsisThis book is designed for undergraduate programs and students and can also be used as a first-year graduate text in probability. It offers a broad perspective, building on the synopsis of measure and integration offered in Chapter two.

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Book SynopsisTable of ContentsCHAPTER 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

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Book SynopsisThe 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).CPTrade ReviewFeatures 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 *Since 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 *Review 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 *One 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 *Table of Contents1: 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

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Book SynopsisThe 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.

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Book Synopsis

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Book SynopsisTaken 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. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.Trade ReviewWinner of the 2005 DeGroot Prize.From the reviews:"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." Technometrics, August 2004"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.'" Biometrics, December 2004"Although All of Statistics 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." The American Statistician, May 2005"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)"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)"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)"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)"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)Table of ContentsProbability.- 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.

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Book SynopsisStructured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.Trade ReviewFrom the reviews:MATHEMATICAL REVIEWS"This is indeed an invaluable text for students in information technology, engineering, and statistics. It is also very helpful for researchers in these fields and for those working in industry. The book is self-contained…The book has enough illustrative examples and exercises for the reader. All the illustrations are motivated by real applications. Moreover, the book provides a good balance between pure mathematical treatment and the applied aspects of the subject.""The Bayesian network (BN), or probabilistic expert system, is technology for automating human-life reasoning under uncertainty in specific contexts. … the book does an admirable job of concisely explaining a great range of concepts and techniques. … the book is very well written and to my knowledge nothing else meets its specific goal of quickly equipping the reader with both practical skills and sufficient theoretical background. … I certainly would not want to try to implement a BN application without reading this book.” (David Tritchler, Sankhya: Indian Journal of Statistics, Vol. 64 (B Part 3), 2002)"Professor Jensen is certainly one of the most influential researchers in the field of Bayesian networks and it is not surprising that this book represents a very clear and useful presentation of the main properties and use of graphical models. … I think that the present volume represents a useful integration of other material and a compact guide for either a student who wants an introduction to the field or a teacher who needs a reference for a course on probabilistic reasoning in AI." (Luigi Portinale, The Computer Journal, Vol. 46 (3), 2003)"This book is an introduction to Bayesian networks at an accessible level for first-year graduate or advanced undergraduate students. … I found this book to be an excellent introduction to the topic. It is well written, provides broad topic coverage, and is quite accessible to the non-expert. … I think Bayesian Networks and Decision Graphs would make a fine text for an introductory class in Bayesian networks or a useful reference for anyone interested in learning about the field." (David J. Marchette, Technometrics, Vol. 45 (2), 2003)"I can comfortably recommend this book as a primary source for topics related to Bayesian networks and decision graphs. This would be an excellent edition to any personal library." (Technometrics, Feburary 2008)From the reviews of the second edition:"The present book provides a very readable but also rigorous and comprehensive introduction to the subject. It would make a very good text for a graduate or an advanced undergraduate course. … Altogether, this is a very useful book for anyone interested in learning Bayesian networks without tears." (Jayanta K. Ghosh, International Statistical Reviews, Vol. 76 (2), 2008)"This book is the second edition of Jensen’s Bayesian Networks and Decision Graphs … . Each chapter ends with a summary section, bibliographic notes, and exercises. … provides a readable, self-contained, and above all, practical introduction to Bayesian networks and decision graphs. Its treatment is appropriate not just for statisticians, but also for computer scientists, engineers, and others researchers with appropriate mathematical background. … highly recommend it as a text or a useful reference for anyone interested in probabilistic graphical models or decision graphs." (Alyson G. Wilson, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)“Devoted to Bayesian Networks or Graphical Models and Influence Diagrams, covering a full course with nice exercises … . It is useful as a reference for special topics. … strongly recommended for readers or user of BNs who are interested in specifying dependency models. … great importance to practitioners who try to find causality behind call-backs of products or crashes. … the book can be recommended to anybody working on the interface of operations research, AI, statistics and computer science.”­­­ (Hans-J. Lenz, Statistical Papers, Vol. 52, 2011)Table of ContentsCausal and Bayesian Networks * Part I: A Practical Guide to Normative Systems: Building Models * Learning, Adaptation, and Tuning * Decision Graphs * Part II: Algorithms for Normative Systems: Belief Updating in Bayesian Networks * Bayesian Network Analysis Tools * Algorithms for Influence Diagrams

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Book SynopsisBasics.- 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.Trade ReviewFrom the reviews:TECHNOMETRICS"…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.""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)"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)"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)"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)"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)From the reviews of the second edition:“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)“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)Table of ContentsBasics. - 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.

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Book SynopsisThis book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy.Trade ReviewFrom the reviews: "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) "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)Table of ContentsThe 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.

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Book SynopsisDifferentiable 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.Table of ContentsDifferentiable 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.

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Book Synopsis A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods. Trade ReviewFrom the reviews:This 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)“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)“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)“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)Table of Contentsand 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.

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Book Synopsis1: Cars, Goats, and Sample Spaces. 2: How to Count: Birthdays andLotteries. 3: Conditional Probability: From Kings to Prisoners. 4: TheFormula of Thomas Bayes and Other Matters. 5: The Idea ofIndependence, with Applications. 6: A Little Bit About Games. 7:Random Variables, Expectations, and More About Games. 8: BaseballCards, The Law of Large Numbers, and Bad News for Gamblers. 9: FromTraffic to Chocolate Chip Cookies with the Poisson Distribution. 10:The Desperate Case of the Gambler's Ruin. 11: Breaking Sticks, TossingNeedles, and More: Probability on Continuous Sample Spaces. 12: NormalDistribution, and Order from Diversity via the Central Limit Theorem.13: Random Numbers: What They Are and How to Use Them. 14: Computersand Probability. 15: Statistics: Applying Probability to MakeDecisions. 16: Roaming the Number Line with a Markov Chain:Dependence. 17: The Brownian Motion, and Other Processes in ContinuousTime.Table of Contents1 Cars, Goats, and Sample Spaces.- 1.1 Getting your goat.- 1.2 Nutshell history and philosophy lesson.- 1.3 Let those dice roll. Sample spaces.- 1.4 Discrete sample spaces. Probability distributions and spaces.- 1.5 The car-goat problem solved.- 1.6 Exercises for Chapter 1.- 2 How to Count: Birthdays and Lotteries.- 2.1 Counting your birthdays.- 2.2 Following your dreams in Lottoland.- 2.3 Exercises for Chapter 2.- 3 Conditional Probability: From Kings to Prisoners.- 3.1 Some probability rules. Conditional Probability.- 3.2 Does the king have a sister?.- 3.3 The prisoner’s dilemma.- 3.4 All about urns.- 3.5 Exercises for Chapter 3.- 4. The Formula of Thomas Bayes and Other Matters.- 4.1 On blood tests and Bayes’s formula.- 4.2 An urn problem.- 4.3 Laplace’s law of succession.- 4.4 Subjective probability.- 4.5 Questions of paternity.- 4.6 Exercises for Chapter 4.- 5 The Idea of Independence, with Applications.- 5.1 Independence of events.- 5.2 Waiting for the first head to show.- 5.3 On the likelihood of alien life.- 5.4 The monkey at the typewriter.- 5.5 Rare events do occur.- 5.6 Rare versus extraordinary events.- 5.7 Exercises for Chapter 5.- 6 A Little Bit About Games.- 6.1 The problem of points.- 6.2 Craps.- 6.3 Roulette.- 6.4 What are the odds?.- 6.5 Exercises for Chapter 6.- 7 Random Variables, Expectations, and More About Games.- 7.1 Random variables.- 7.2 The binomial random variable.- 7.3 The game of chuck-a-luck and de Méré’s problem of dice.- 7.4 The expectation of a random variable.- 7.5 Fair and unfair games.- 7.6 Gambling systems.- 7.7 Administering a blood test.- 7.8 Exercises for Chapter 7.- 8 Baseball Cards, The Law of Large Numbers, and Bad News for Gamblers.- 8.1 The coupon collector’s problem.- 8.2 Indicator variables and the expectation of a binomial variable.- 8.3 Independent random variables.- 8.4 The coupon collector’s problem solved.- 8.5 The Law of Large Numbers.- 8.6 The Law of Large Numbers and gambling.- 8.7 A gambler’s fallacy.- 8.8 The variance of a random variable.- 8.8.1 Appendix.- 8.8.2 The variance of the sum of independent random variables.- 8.8.3 The variance ofSn/n.- 8.9 Exercises for Chapter 8.- 9 From Traffic to Chocolate Chip Cookies with the Poisson Distribution.- 9.1 A traffic problem.- 9.2 The Poisson as an approximation to the binomial.- 9.3 Applications of the Poisson distribution.- 9.4 The Poisson process.- 9.5 Exercises for Chapter 9.- 10 The Desperate Case of the Gambler’s Ruin.- 10.1 Let’s go for a random walk.- 10.2 The gambler’s ruin problem.- 10.3 Bold play or timid play?.- 10.4 Exercises for Chapter 10.- 11 Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces.- 11.1 Choosing a number at random from an interval.- 11.2 Bus stop.- 11.3 The expectation of a continuous random variable.- 11.4 Normal numbers.- 11.5 Bertrand’s paradox.- 11.6 When do we have a triangle?.- 11.7 Buffon’s needle problem.- 11.8 Exercises for Chapter 11.- 12 Normal Distributions, and Order from Diversity via the Central Limit Theorem.- 12.1 Making sense of some data.- 12.2 The normal distributions.- 12.3 Some pleasant properties of normal distributions.- 12.4 The Central Limit Theorem.- 12.5 How many heads did you get?.- 12.6 Why so many quantities may be approximately normal.- 12.7 Exercises for Chapter 12.- 13 Random Numbers: What They Are and How to Use Them.- 13.1 What are random numbers?.- 13.2 When are digits random? Statistical randomness.- 13.3 Pseudo-random numbers.- 13.4 Random sequences arising from decimal expansions.- 13.5 The use of random numbers.- 13.6 The 1970 draft lottery.- 13.7 Exercises for Chapter 13.- 14 Computers and Probability.- 14.1 A little bit about computers.- 14.2 Frequency of zeros in a random sequence.- 14.3 Simulation of tossing a coin.- 14.4 Simulation of rolling a pair of dice.- 14.5 Simulation of the Buffon needle tosses.- 14.6 Monte Carlo estimate of ? using bombardment of a circle.- 14.7 Monte Carlo estimate for the broken stick problem.- 14.8 Monte Carlo estimate of a binomial probability.- 14.9 Monte Carlo estimate of the probability of winning at craps.- 14.10 Monte Carlo estimate of the gambler’s ruin probability.- 14.11 Constructing approximately normal random variables.- 14.12 Exercises for Chapter 14.- 15 Statistics: Applying Probability to Make Decisions.- 15.1 What statistics does.- 15.2 Lying with statistics?.- 15.3 Deciding between two probabilities.- 15.4 More complicated decisions.- 15.5 How many fish in the lake, and other problems of estimation.- 15.6 Polls and confidence intervals.- 15.7 Random sampling.- 15.8 Some concluding remarks.- 15.9 Exercises for Chapter 15.- 16 Roaming the Number Line with a Markov Chain: Dependence.- 16.1 A picnic in Alphaville?.- 16.2 One-dimensional random walks.- 16.3 The probability of ever returning “home”.- 16.4 About the gambler recouping her losses.- 16.5 The dying out of family names.- 16.6 The number of parties waiting for a taxi.- 16.7 Stationary distributions.- 16.8 Applications to genetics.- 16.9 Exercises for Chapter 16.- 17 The Brownian Motion, and Other Processes in Continuous Time.- 17.1 Processes in continuous time.- 17.2 A few computations for the Poisson process.- 17.3 The Brownian motion process.- 17.4 A few computations for Brownian motion.- 17.5 Brownian motion as a limit of random walks.- 17.6 Exercises for Chapter 17.- Answers to Exercises.

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Book SynopsisI: The Dichotomous Rasch Model.- 1. Some Background for Item Response Theory and the Rasch Model.- 2. Derivations of the Rasch Model.- 3. Estimation of Item Parameters.- 4. On Person Parameter Estimation in the Dichotomous Rasch Model.- 5. Testing the Rasch Model.- 6. The Assessment of Person Fit.- 7. Test Construction from Item Banks.- II: Extensions of the Dichotomous Rasch Model.- 8. The Linear Logistic Test Model.- 9. Linear Logistic Models for Change.- 10. Dynamic Generalizations of the Rasch Model.- 11. Linear and Repeated Measures Models for the Person Parameters.- 12. The One Parameter Logistic Model.- 13. Linear Logistic Latent Class Analysis and the Rasch Model.- 14. Mixture Distribution Rasch Models.- III: Polytomous Rasch Models and their Extensions.- 15. Polytomous Rasch Models and their Estimation.- 16. The Derivation of Polytomous Rasch Models.- 17. The Polytomous Rasch Model within the Class of Generalized Linear Symmetry Models.- 18. Tests of Fit for Polytomous Rasch MTable of ContentsI: The Dichotomous Rasch Model.- 1. Some Background for Item Response Theory and the Rasch Model.- 2. Derivations of the Rasch Model.- 3. Estimation of Item Parameters.- 4. On Person Parameter Estimation in the Dichotomous Rasch Model.- 5. Testing the Rasch Model.- 6. The Assessment of Person Fit.- 7. Test Construction from Item Banks.- II: Extensions of the Dichotomous Rasch Model.- 8. The Linear Logistic Test Model.- 9. Linear Logistic Models for Change.- 10. Dynamic Generalizations of the Rasch Model.- 11. Linear and Repeated Measures Models for the Person Parameters.- 12. The One Parameter Logistic Model.- 13. Linear Logistic Latent Class Analysis and the Rasch Model.- 14. Mixture Distribution Rasch Models.- III: Polytomous Rasch Models and their Extensions.- 15. Polytomous Rasch Models and their Estimation.- 16. The Derivation of Polytomous Rasch Models.- 17. The Polytomous Rasch Model within the Class of Generalized Linear Symmetry Models.- 18. Tests of Fit for Polytomous Rasch Models.- 19. Extended Rating Scale and Partial Credit Models for Assessing Change.- 20. Polytomous Mixed Rasch Models.- In Retrospect.- 21. What Georg Rasch Would Have Thought about this Book.- References.- Author Index.- Abbreviations.

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Book SynopsisThe aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D.Trade ReviewFrom the reviews: "Another excellent book in theory of statistics is by Mark J. Schervish. … Readers will enjoy reading this book to see how differently the theory can be presented … . This well written book contains nine chapters and four appendices. ... Each chapter has both easy and challenging problems. The book is suitable for graduate level statistical theory courses. Examples and illustrations are well explained. I liked the author’s presentation, and learned a lot from the book. I highly recommend this book to theoretical statisticians." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (11), November, 2004)Table of ContentsContent.- 1: Probability Models.- 1.1 Background.- 1.1.1 General Concepts.- 1.1.2 Classical Statistics.- 1.1.3 Bayesian Statistics.- 1.2 Exchangeability.- 1.2.1 Distributional Symmetry.- 1.2.2 Frequency arid Exchangeability.- 1.3 Parametric Models.- 1.3.1 Prior, Posterior, and Predictive Distributions.- 1.3.2 Improper Prior Distributions.- 1.3.3 Choosing Probability Distributions.- 1.4 DeFinetti’s Representation Theorem.- 1.4.1 Understanding the Theorems.- 1.4.2 The Mathematical Statements.- 1.4.3 Some Examples.- 1.5 Proofs of DeFinetti’s Theorem and Related Results*.- 1.5.1 Strong Law of Large Numbers.- 1.5.2 The Bernoulli Case.- 1.5.3 The General Finite Case*.- 1.5.4 The General Infinite Case.- 1.5.5 Formal Introduction to Parametric Models*.- 1.6 Infinite-Dimensional Parameters*.- 1.6.1 Dirichlet Processes.- 1.6.2 Tailfree Processes+.- 1.7 Problems.- 2: Sufficient Statistics.- 2.1 Definitions.- 2.1.1 Notational Overview.- 2.1.2 Sufficiency.- 2.1.3 Minimal and Complete Sufficiency.- 2.1.4 Ancillarity.- 2.2 Exponential Families of Distributions.- 2.2.1 Basic Properties.- 2.2.2 Smoothness Properties.- 2.2.3 A Characterization Theorem*.- 2.3 Information.- 2.3.1 Fisher Information.- 2.3.2 Kullback-Leibler Information.- 2.3.3 Conditional Information*.- 2.3.4 Jeffreys’ Prior*.- 2.4 Extremal Families*.- 2.4.1 The Main Results.- 2.4.2 Examples.- 2.4.3 Proofs+.- 2.5 Problems.- Chapte 3: Decision Theory.- 3.1 Decision Problems.- 3.1.1 Framework.- 3.1.2 Elements of Bayesian Decision Theory.- 3.1.3 Elements of Classical Decision Theory.- 3.1.4 Summary.- 3.2 Classical Decision Theory.- 3.2.1 The Role of Sufficient Statistics.- 3.2.2 Admissibility.- 3.2.3 James—Stein Estimators.- 3.2.4 Minimax Rules.- 3.2.5 Complete Classes.- 3.3 Axiomatic Derivation of Decision Theory*.- 3.3.1 Definitions and Axioms.- 3.2.2 Examples.- 3.3.3 The Main Theorems.- 3.3.4 Relation to Decision Theory.- 3.3.5 Proofs of the Main Theorems*.- 3.3.6 State-Dependent Utility*.- 3.4 Problems.- 4: Hypothesis Testing.- 4.1 Introduction.- 4.1.1 A Special Kind of Decision Problem.- 4.1.2 Pure Significance Tests.- 4.2 Bayesian Solutions.- 4.2.1 Testing in General.- 4.2.2 Bayes Factors.- 4.3 Most Powerful Tests.- 4.3.1 Simple Hypotheses and Alternatives.- 4.3.2 Simple Hypotheses, Composite Alternatives.- 4.3.3 One-Sided Tests.- 4.3.4 Two-Sided Hypotheses.- 4.4 Unbiased Tests.- 4.4.1 General Results.- 4.4.2 Interval Hypotheses.- 4.4.3 Point Hypotheses.- 4.5 Nuisance Parameters.- 4.5.1 Neyinan Structure.- 4.5.2 Tests about Natural Parameters.- 4.5.3 Linear Combinations of Natural Parameters.- 4.5.4 Other Two-Sided Cases*.- 4.5.5 Likelihood Ratio Tests.- 4.5.6 The Standard F-Test as a Bayes Rule.- 4.6 P-Values.- 4.6.1 Definitions and Examples.- 4.6.2 P-Values and Bayes Factors.- 4.7 Problems.- 5: Estimation.- 5.1 Point Estimation.- 5.1.1 Minimum Variance Unbiased Estimation.- 5.1.2 Lower Bounds on the Variance of Unbiased Estimators.- 5.1.3 Maximum Likelihood Estimation.- 5.1.4 Bayesian Estimation.- 5.1.5 Robust Estimation*.- 5.2 Set Estimation.- 5.2.1 Confidence Sets.- 5.2.2 Prediction Sets*.- 5.2.3 Tolerance Sets*.- 5.2.4 Bayesian Set Estimation.- 5.2.5 Decision Theoretic Set Estimation.- 5.3 The Bootstrap*.- 5.3.1 The General Concept.- 5.3.2 Standard Deviations and Bias.- 5.3.3 Bootstrap Confidence Intervals.- 5.4 Problems.- 6: Equivariance*.- 6.1 Common Examples.- 6.1.1 Location Problems.- 6.1.2 Scale Problems.- 6.2 Equivariant Decision Theory.- 6.2.1 Groups of Transformations.- 6.2.2 Equivariance and Changes of Units.- 6.2.3 Minimum Risk Equivariant Decisions.- 6.3 Testing and Confidence Intervals*.- 6.3.1 P-Values in Invariant Problems.- 6.3.2 Equivariant Confidence Sets.- 6.3.3 Invariant Tests*.- 6.4 Problems.- 7: Large Sample Theory.- 7.1 Convergence Concepts.- 7.1.1 Deterministic Convergence.- 7.1.2 Stochastic Convergence.- 7.1.3 The Delta Method.- 7.2 Sample Quantiles.- 7.2.1 A Single Quantile.- 7.2.2 Several Quantiles.- 7.2.3 Linear Combinations of Quantiles*.- 7.3 Large Sample Estimation.- 7.3.1 Some Principles of Large Sample Estimation.- 7.3.2 Maximum Likelihood Estimators.- 7.3.3 MLEs in Exponential Families.- 7.3.4 Examples of Inconsistent MLEs.- 7.3.5 Asymptotic Normality of MLEs.- 7.3.6 Asymptotic Properties of M-Estimators.- 7.4 Large Sample Properties of Posterior Distributions.- 7.4.1 Consistency of Posterior Distributions+.- 7.4.2 Asymptotic Normality of Posterior Distributions.- 7.4.3 Laplace Approximations to Posterior Distributions*.- 7.4.4 Asymptotic Agreement of Predictive Distributions+.- 7.5 Large Sample Tests.- 7.5.1 Likelihood Ratio Tests.- 7.5.2 Chi-Squarcd Goodness of Fit Tests.- 7.6 Problems.- 8: Hierarchical Models.- 8.1 Introduction.- 8.1.1 General Hierarchical Models.- 8.1.2 Partial Exchangeability*.- 8.1.3 Examples of the Representation Theorem*.- 8.2 Normal Linear Models.- 8.2.1 One-Way ANOVA.- 8.2.2 Two-Way Mixed Model ANOVA*.- 8.2.3 Hypothesis Testing.- 8.3 Nonnormal Models*.- 8.3.1 Poisson Process Data.- 8.3.2 Bernoulli Process Data.- 8.4 Empirical Bayes Analysis*.- 8.4.1 Naïve Empirical Bayes.- 8.4.2 Adjusted Empirical Bayes.- 8.4.3 Unequal Variance Case.- 8.5 Successive Substitution Sampling.- 8.5.1 The General Algorithm.- 8.5.2 Normal Hierarchical Models.- 8.5.3 Nonnormal Models.- 8.6 Mixtures of Models.- 8.6.1 General Mixture Models.- 8.6.2 Outliers.- 8.6.3 Bayesian Robustness.- 8.7 Problems.- 9: Sequential Analysis.- 9.1 Sequential Decision Problems.- 9.2 The Sequential Probability Ratio Test.- 9.3 Interval Estimation*.- 9.4 The Relevancc of Stopping Rules.- 9.5 Problems.- Appendix A: Measure and Integration Theory.- A.1 Overview.- A.1.1 Definitions.- A.1.2 Measurable Functions.- A.1.3 Integration.- A.1.4 Absolute Continuity.- A.2 Measures.- A.3 Measurable Functions.- A.4 Integration.- A.5 Product Spaces.- A.6 Absolute Continuity.- A.7 Problems.- Appendix B: Probability Theory.- B.1 Overview.- B.1.1 Mathematical Probability.- B.1.2 Conditioning.- B.1.3 Limit Theorems.- B.2 Mathematical Probability.- B.2.1 Random Quantities and Distributions.- B.2.2 Some Useful Inequalities.- B.3 Conditioning.- B.3.1 Conditional Expectations.- B.3.2 Borel Spaces*.- B.3.3 Conditional Densities.- B.3.4 Conditional Independence.- B.3.5 The Law of Total Probability.- B.4 Limit Theorems.- B.4.1 Convergence in Distribution and in Probability.- B.4.2 Characteristic Functions.- B.5 Stochastic Processes.- B.5.1 Introduction.- B.5.3 Markov Chains*.- B.5.4 General Stochastic Processes.- B.6 Subjective Probability.- B.7 Simulation*.- B.8 Problems.- Appendix C: Mathematical Theorems Not Proven Here.- C.1 Real Analysis.- C.2 Complex Analysis.- C.3 Functional Analysis.- Appendix D: Summary of Distributions.- D.1 Univariate Continuous Distributions.- D.2 Univariate Discrete Distributions.- D.3 Multivariate Distributions.- References.- Notation and Abbreviation Index.- Name Index.

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Book SynopsisExamples.- A Model for Longitudinal Data.- Exploratory Data Analysis.- Estimation of the Marginal Model.- Inference for the Marginal Model.- Inference for the Random Effects.- Fitting Linear Mixed Models with SAS.- General Guidelines for Model Building.- Exploring Serial Correlation.- Local Influence for the Linear Mixed Model.- The Heterogeneity Model.- Conditional Linear Mixed Models.- Exploring Incomplete Data.- Joint Modeling of Measurements and Missingness.- Simple Missing Data Methods.- Selection Models.- Pattern-Mixture Models.- Sensitivity Analysis for Selection Models.- Sensitivity Analysis for Pattern-Mixture Models.- How Ignorable Is Missing At Random ?.- The Expectation-Maximization Algorithm.- Design Considerations.- Case Studies.Trade ReviewFrom the reviews: MATHEMATICAL REVIEWS "This book emphasizes practice rather than mathematical rigor and the majority of the chapters are explanatory rather than research oriented. In this respect, guidance and advice on practical issues are the main focus of the text. Hence it will be of interest to applied statisticians and biomedical researchers in industry, particularly in the pharmaceutical industry, medical public health organizations, contract research organizations, and academia." "This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Over 125 illustrations are included in the book. … I do believe that the book may serve as a useful reference to a broader audience. Since practical examples are provided as well as discussion of the leading software utilization, it may also be appropriate as a textbook in an advanced undergraduate-level or a graduate-level course in an applied statistics program." (Ana Ivelisse Avil és, Technometrics, Vol. 43 (3), 2001) "A practical book with a great many examples, including worked computer code and access to the datasets. … The authors state that the book covers ‘linear mixed models for continuous outcomes’ … . The book has four main strengths: its practical bent, its emphasis on exploratory analysis, its description of tools for model checking, and its treatment of dropout and missingness … . my impression of the book was … positive. Its strong practical nature and emphasis on dropout modelling are particularly welcome … ." (Harry Southworth, ISCB Newsletter, June, 2002) "This book is devoted to linear mixed-effects models with strong emphasis on the SAS procedure. Guidance and advice on practical issues are the main focus of the text. … It is of value to applied statisticians and biomedical researchers. … I recommend this book as a reference to applied statisticians and biomedical researchers, particularly in the pharmaceutical industry, medical and public organizations." (Wang Songgui, Zentralblatt MATH, Vol. 956, 2001)Table of ContentsIntroduction * Examples * A model for Longitudinal Data * Exploratory Data Analysis * Estimation of the Marginal Model * Inference for the Marginal Model * Inference for the Random Effects * Fitting Linear Mixed Models with SAS * General Guidelines for Model Building * Exploring Serial Correlation * Local Influence for the Linear Mixed Model * The Heterogeneity Model * Conditional Linear Mixed Models * Exploring Incomplete Data * Joint Modeling of Measurements and Missingness * Simple Missing Data Methods * Selection Models * Pattern-Mixture Models * Sensitivity Analysis for Selection Models * Sensitivity Analysis for Models * How Ignorable is Missing at Random? * The Expectation-Maximization Algorithm * Design Considerations * Case Studies

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Book SynopsisA comprehensive introduction to a wide variety of statistical methods for the analysis of repeated measurements. It is designed to be both a useful reference for practitioners and a textbook for a graduate-level course focused on methods for the analysis of repeated measurements.Trade ReviewFrom the reviews: MATHEMATICAL REVIEWS "…the book covers a wide range of topics, including inference based on normal theory, repeated categorical outcomes and missing values. The book is based on lecture notes used by the author since 1991. Hence, the material and the structure of the book have been well tested by different audiences. Another feature of the book is the inclusion of a very rich collection of problems with excellent real data. Thus, it is a nice textbook for a semester course on repeated measurements and longitudinal data." SHORT BOOK REVIEW "Each major topic is introduced logically; background theory is clearly elucidated, and at least one example is carefully worked in detail. The use of eighty real sets of data, given in full, is a most attractive feature. Attention is concentrated on those techniques that are most readily available in software. ... This should prove to be a very useful text for teacher, student and practitioner alike." JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION "Most other books on repeated measurements tend to focus on specialized topics. In my opinion, [this] book is the most comprehensive and readable of the lot. I would highly recommend its use as a text for a semester-length graduate course for biostatistics and statistics students and also as resource book for consulting biostatisticians and statisticians. In addition, this book would be a valuable resource for students from other fields of study (e.g., the health sciences) who have a statistical aptitude. The book is definitely worth the price." "The intention of the book is ‘to provide a reasonably comprehensive overview of methods for the analysis of repeated measurements’ with focus on standard statistical methods … . In my opinion the book gives a nice, comprehensive overview of methods for the analysis of repeated measurements. … The availability of data sets, overheads, etc. is a very valuable supplement for both teachers and students. … The book … could be a natural choice for a course in repeated measurements for graduate students in (bio-) statistics." (Niels Trolle Andersen, Statistics in Medicine, Vol. 24 (5), 2005) "This book is a very interesting and comprehensive summary of a wide selection of statistical methods for the analysis of repeated measurements. It is indeed an ideal and carefully written text to be used as a reference guide for practitioners and, in addition, as a great, up to date and very complete textbook for a graduate-level course in Statistics and/or Biostatistics. … I highly recommend Statistical Methods … as a good reference book for anyone interested in looking into the different available methodologies … ." (Vicente Núñez-Antón, Journal of Applied Statistics, Vol. 30 (10), December, 2003) "This book provides a comprehensive introduction to a wide variety of statistical methods for the analysis of repeated measurements. … In conclusion, as a course text on repeated measurements this book clearly has major strengths over others in that it provides coverage on a wide range of topics and provides extensive further reading material. … I would recommend this text as a general reference book on repeated measurements which would make a worthwhile addition to a departmental library." (Fiona Holland, Pharmaceutical Statistics, 2003) "Most other books on repeated measurements … tend to focus on specialized topics. In my opinion, Statistical Methods for the Analysis of Repeated Measurements book is the most comprehensive and readable of the lot. I would highly recommend its use as a text for a semester-length graduate course for biostatistics and statistics students and … for consulting biostatisticians and statisticians. … a valuable resource for students from other fields of study … who have a statistical aptitude. The book is definitely worth the price." (Melvin L. Moeschberger, Journal of the American Statistical Association, March, 2003) "The book aims at describing, discussing and demonstrating a variety of statistical methods for the analysis of repeated measurements … . the book covers a very wide range of topics, including inference based on normal theory, repeated categorical outcomes and missing values. … Another feature of the book is the inclusion of a very rich collection of problems with excellent real data. Thus, it is a nice textbook for a semester course on repeated measurements and longitudinal data." (Jack C. Lee, Mathematical Reviews, 2003 e) "This book is intended to provide a comprehensive introduction to a wide range of statistical methods for the analysis of repeated measurements. … For use in a course, I would use it for an applied graduate-level statistics course on linear models for analysis of repeated measurements. This text is useful not only with regards to the statistical methods, but also for the real data examples that can be explored with the various models and methods under study." (James R. Kenyon, Technometrics, Vol. 45 (1), 2003) "This book provides a reasonably comprehensive overview of a wide variety of statistical methods for the analysis of repeated measurements … . The important features of this book include a summary of both classical and recent methods for continuous and categorical outcome variables, numerous homework problems, and the extensive use of real data sets in examples. … This book will be of interest to graduate students in statistics and biostatistics as well as to practicing statisticians in academic, industry and research institutions.” (Ivan Krivý, Zentralblatt MATH, Vol. 985, 2002)Table of ContentsIntroduction * Univariate Methods * Normal-Theory Methods: Unstructured Multivariate Approach * Normal Theory Methods: Multivariate Analysis of Variance * Normal-Theory Methods: Repeated Measures ANOVA * Normal Theory Methods: Linear Mixed Models * Weighted Least Squares Analysis of Repeated Categorical Outcomes * Randomization Model Methods for One-Sample Repeated Measurements * Methods Based on Extensions of Generalized Linear Models * Nonparametric Methods

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Book SynopsisPoint processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology. This volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction.Trade ReviewFrom the reviews of the second edition: "This is an important treatise on the mathematical theory relevant to a wide variety of random processes…The reader will find excellent treatments of important advanced topics such as Cox, renewal, Wold, marked, cluster, and other specialized processes, plus concise but useful appendices on topology, measure theory, metric spaces, martingales, and the like." Technometrics, May 2004 "This revision splits the lengthy first version into two volumes now subtitled Volume I: Elementary Theory and Methods and Volume II: Models and General Theory and Structure...this first volume is well worth its price." Journal of the American Statistical Association, September 2004 "The theory of point processes has undergone an explosive expansion in the last two decades. There was a genuine need for a single source that would contain a survey of the general theory of Point Process accessible to beginning graduate students and researchers in the field but at the same time would include some of the more recent – though relatively advanced and technically difficult – developments in the area. The present edition of the book addresses that need quite successfully.” (Alok Goswami, Sankhya, Vol. 67 (1), 2005) "It is a pleasure to announce that a second edition of the classic book ‘An Introduction to the Theory of Point Processes’ has been published. … many chapters and sections were thoroughly reworked. This holds true in particular for the exercises, which are obviously produced with particular love. … The reviewer is sure that the owners of the first edition will buy also the second, and for many younger readers it will become the beloved key reference to point processes." (Dietrich Stoyan, Metrika, May, 2004) "The second edition of this monograph is divided into two volumes. The first one is concentrated on introductory material and models, the second one on structure and general theory. … suitable as a textbook with many exercises for beginners as well as a source for scientists interested in high level applications of point processes." (Uwe Küchler, Zentralblatt MATH, Vol. 1026, 2004) "The first edition of this book by two major research workers in the field speedily established itself as an authoritative account of an important and rapidly developing subject. In this substantially revised and expanded second edition, the authors have wisely decided to divide the book into two parts leaving some of the very technical material … to a second volume. … The book is likely to establish itself quickly as a major contribution to the field." (D. R. Cox, Short Book Reviews, Vol. 23 (2), 2003)Table of ContentsEarly History * Basic Properties of the Poisson Process * Simple Results for Stationary Point Processes on the Line * Renewal Processes * Finite Point Processes * Models Constructed via Conditioning: Cox, Cluster,and Marked Point Processes * Conditional Intensities and Likelihoods * Second Order Properties of Stationary Point Processes

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Book Synopsis1 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 expectationTrade Review"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."Short Book Reviews, Vol. 23/3, Dec. 2003 "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 From the reviews of the fourth edition: "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)Table of ContentsSet * 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

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Book Synopsis1 Controlled Markov Processes.- 1.1 Introduction.- 1.2 Stochastic Control Problems.- 1.3 Examples.- 1.4 Further Comments.- 2 Discounted Reward Criterion.- 2.1 Introduction.- 2.2 Optimality Conditions.- 2.3 Asymptotic Discount Optimality.- 2.4 Approximation of MCM's.- 2.5 Adaptive Control Models.- 2.6 Nonparametric Adaptive Control.- 2.7 Comments and References.- 3 Average Reward Criterion.- 3.1 Introduction.- 3.2 The Optimality Equation.- 3.3 Ergodicity Conditions.- 3.4 Value Iteration.- 3.5 Approximating Models.- 3.6 Nonstationary Value Iteration.- 3.7 Adaptive Control Models.- 3.8 Comments and References.- 4 Partially Observable Control Models.- 4.1 Introduction.- 4.2 PO-CM: Case of Known Parameters.- 4.3 Transformation into a CO Control Problem.- 4.4 Optimal I-Policies.- 4.5 PO-CM's with Unknown Parameters.- 4.6 Comments and References.- 5 Parameter Estimation in MCM's.- 5.1 Introduction.- 5.2 Contrast Functions.- 5.3 Minimum Contrast Estimators.- 5.4 Comments and References.- 6 Discretization Procedures.- 6.1 Introduction.- 6.2 Preliminaries.- 6.3 The Non-Adaptive Case.- 6.4 Adaptive Control Problems.- 6.5 Proofs.- 6.6 Comments and References.- Appendix A. Contraction Operators.- Appendix B. Probability Measures.- Total Variation Norm.- Weak Convergence.- Appendix C. Stochastic Kernels.- Appendix D. Multifunctions and Measurable Selectors.- The Hausdorff Metric.- Multifunctions.- References.- Author Index.Table of Contents1 Controlled Markov Processes.- 1.1 Introduction.- 1.2 Stochastic Control Problems.- Control Models.- Policies.- Performance Criteria.- Control Problems.- 1.3 Examples.- An Inventory/Production System.- Control of Water Reservoirs.- Fisheries Management.- Nonstationary MCM’s.- Semi-Markov Control Models.- 1.4 Further Comments.- 2 Discounted Reward Criterion.- 2.1 Introduction.- Summary.- 2.2 Optimality Conditions.- Continuity of ?*.- 2.3 Asymptotic Discount Optimality.- 2.4 Approximation of MCM’s.- Nonstationary Value-Iteration.- Finite-State Approximations.- 2.5 Adaptive Control Models.- Preliminaries.- Nonstationary Value-Iteration.- The Principle of Estimation and Control.- Adaptive Policies.- 2.6 Nonparametric Adaptive Control.- The Parametric Approach.- New Setting.- The Empirical Distribution Process.- Nonparametric Adaptive Policies.- 2.7 Comments and References.- 3 Average Reward Criterion.- 3.1 Introduction.- Summary.- 3.2 The Optimality Equation.- 3.3 Ergodicity Conditions.- 3.4 Value Iteration.- Uniform Approximations.- Successive Averagings.- 3.5 Approximating Models.- 3.6 Nonstationary Value Iteration.- Nonstationary Successive Averagings.- Discounted-Like NVI.- 3.7 Adaptive Control Models.- Preliminaries.- The Principle of Estimation and Control (PEC).- Nonstationary Value Iteration (NVI).- 3.8 Comments and References.- 4 Partially Observable Control Models.- 4.1 Introduction.- Summary.- 4.2 PO-CM: Case of Known Parameters.- The PO Control Problem.- 4.3 Transformation into a CO Control Problem.- I-Policies.- The New Control Model.- 4.4 Optimal I-Policies.- 4.5 PO-CM’s with Unknown Parameters.- PEC and NVI I-Policies.- 4.6 Comments and References.- 5 Parameter Estimation in MCM’s.- 5.1 Introduction.- Summary.- 5.2 Contrast Functions.- 5.3 Minimum Contrast Estimators.- 5.4 Comments and References.- 6 Discretization Procedures.- 6.1 Introduction.- Summary.- 6.2 Preliminaries.- 6.3 The Non-Adaptive Case.- A Non-Recursive Procedure.- A Recursive Procedure.- 6.4 Adaptive Control Problems.- Preliminaries.- Discretization of the PEC Adaptive Policy.- Discretization of the NVI Adaptive Policy.- 6.5 Proofs.- The Non-Adaptive Case.- The Adaptive Case.- 6.6 Comments and References.- Appendix A. Contraction Operators.- Appendix B. Probability Measures.- Total Variation Norm.- Weak Convergence.- Appendix C. Stochastic Kernels.- Appendix D. Multifunctions and Measurable Selectors.- The Hausdorff Metric.- Multifunctions.- References.- Author Index.

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Book Synopsis1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- 1.4. The DoobMeyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- 2.5. The Markov Property.- 2.6. The Strong Markov Property and the Reflection Principle.- 2.7. Brownian Filtrations.- 2.8. Computations Based on Passage Times.- 2.9. The Brownian Sample Paths.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- 3.3. The Change-of-Variable Formula.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- 3.5. The Girsanov Theorem.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- 4.3. The One-Dimensional Heat Equation.- 4.4. The Formulas of Feynman and Kac.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- 5.3. Weak Solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- 5.5. A Study of the One-Dimensional Case.- 5.6. Linear Equations.- 5.7. Connections with Partial Differential Equations.- 5.8. Applications to Economics.- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy's Theory of Brownian Local Time.-6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- 6.3. Two Independent Reflected Brownian Motions.- 6.4. Elastic Brownian Motion.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.Trade ReviewSecond Edition I. Karatzas and S.E. Shreve Brownian Motion and Stochastic Calculus "A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."—MATHEMATICAL REVIEWSTable of Contents1 Martingales, Stopping Times, and Filtrations.- 1.1. Stochastic Processes and ?-Fields.- 1.2. Stopping Times.- 1.3. Continuous-Time Martingales.- A. Fundamental inequalities.- B. Convergence results.- C. The optional sampling theorem.- 1.4. The Doob—Meyer Decomposition.- 1.5. Continuous, Square-Integrable Martingales.- 1.6. Solutions to Selected Problems.- 1.7. Notes.- 2 Brownian Motion.- 2.1. Introduction.- 2.2. First Construction of Brownian Motion.- A. The consistency theorem.- B. The Kolmogorov—?entsov theorem.- 2.3. Second Construction of Brownian Motion.- 2.4. The SpaceC[0, ?), Weak Convergence, and Wiener Measure.- A. Weak convergence.- B. Tightness.- C. Convergence of finite-dimensional distributions.- D. The invariance principle and the Wiener measure.- 2.5. The Markov Property.- A. Brownian motion in several dimensions.- B. Markov processes and Markov families.- C. Equivalent formulations of the Markov property.- 2.6. The Strong Markov Property and the Reflection Principle.- A. The reflection principle.- B. Strong Markov processes and families.- C. The strong Markov property for Brownian motion.- 2.7. Brownian Filtrations.- A. Right-continuity of the augmented filtration for a strong Markov process.- B. A “universal” filtration.- C. The Blumenthal zero-one law.- 2.8. Computations Based on Passage Times.- A. Brownian motion and its running maximum.- B. Brownian motion on a half-line.- C. Brownian motion on a finite interval.- D. Distributions involving last exit times.- 2.9. The Brownian Sample Paths.- A. Elementary properties.- B. The zero set and the quadratic variation.- C. Local maxima and points of increase.- D. Nowhere differentiability.- E. Law of the iterated logarithm.- F. Modulus of continuity.- 2.10. Solutions to Selected Problems.- 2.11. Notes.- 3 Stochastic Integration.- 3.1. Introduction.- 3.2. Construction of the Stochastic Integral.- A. Simple processes and approximations.- B. Construction and elementary properties of the integral.- C. A characterization of the integral.- D. Integration with respect to continuous, local martingales.- 3.3. The Change-of-Variable Formula.- A. The Itô rule.- B. Martingale characterization of Brownian motion.- C. Bessel processes, questions of recurrence.- D. Martingale moment inequalities.- E. Supplementary exercises.- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion.- A. Continuous local martingales as stochastic integrals with respect to Brownian motion.- B. Continuous local martingales as time-changed Brownian motions.- C. A theorem of F. B. Knight.- D. Brownian martingales as stochastic integrals.- E. Brownian functionals as stochastic integrals.- 3.5. The Girsanov Theorem.- A. The basic result.- B. Proof and ramifications.- C. Brownian motion with drift.- D. The Novikov condition.- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion.- A. Definition of local time and the Tanaka formula.- B. The Trotter existence theorem.- C. Reflected Brownian motion and the Skorohod equation.- D. A generalized Itô rule for convex functions.- E. The Engelbert—Schmidt zero-one law.- 3.7. Local Time for Continuous Semimartingales.- 3.8. Solutions to Selected Problems.- 3.9. Notes.- 4 Brownian Motion and Partial Differential Equations.- 4.1. Introduction.- 4.2. Harmonic Functions and the Dirichlet Problem.- A. The mean-value property.- B. The Dirichlet problem.- C. Conditions for regularity.- D. Integral formulas of Poisson.- E. Supplementary exercises.- 4.3. The One-Dimensional Heat Equation.- A. The Tychonoff uniqueness theorem.- B. Nonnegative solutions of the heat equation.- C. Boundary crossing probabilities for Brownian motion.- D. Mixed initial/boundary value problems.- 4.4. The Formulas of Feynman and Kac.- A. The multidimensional formula.- B. The one-dimensional formula.- 4.5. Solutions to selected problems.- 4.6. Notes.- 5 Stochastic Differential Equations.- 5.1. Introduction.- 5.2. Strong Solutions.- A. Definitions.- B. The Itô theory.- C. Comparison results and other refinements.- D. Approximations of stochastic differential equations.- E. Supplementary exercises.- 5.3. Weak Solutions.- A. Two notions of uniqueness.- B. Weak solutions by means of the Girsanov theorem.- C. A digression on regular conditional probabilities.- D. Results of Yamada and Watanabe on weak and strong solutions.- 5.4. The Martingale Problem of Stroock and Varadhan.- A. Some fundamental martingales.- B. Weak solutions and martingale problems.- C. Well-posedness and the strong Markov property.- D. Questions of existence.- E. Questions of uniqueness.- F. Supplementary exercises.- 5.5. A Study of the One-Dimensional Case.- A. The method of time change.- B. The method of removal of drift.- C. Feller’s test for explosions.- D. Supplementary exercises.- 5.6. Linear Equations.- A. Gauss—Markov processes.- B. Brownian bridge.- C. The general, one-dimensional, linear equation.- D. Supplementary exercises.- 5.7. Connections with Partial Differential Equations.- A. The Dirichlet problem.- B. The Cauchy problem and a Feynman—Kac representation.- C. Supplementary exercises.- 5.8. Applications to Economics.- A. Portfolio and consumption processes.- B. Option pricing.- C. Optimal consumption and investment (general theory).- D. Optimal consumption and investment (constant coefficients).- 5.9. Solutions to Selected Problems.- 5.10. Notes.- 6 P. Lévy’s Theory of Brownian Local Time.- 6.1. Introduction.- 6.2. Alternate Representations of Brownian Local Time.- A. The process of passage times.- B. Poisson random measures.- C. Subordinators.- D. The process of passage times revisited.- E. The excursion and downcrossing representations of local time.- 6.3. Two Independent Reflected Brownian Motions.- A. The positive and negative parts of a Brownian motion.- B. The first formula of D. Williams.- C. The joint density of (W(t), L(t), ? +(t)).- 6.4. Elastic Brownian Motion.- A. The Feynman—Kac formulas for elastic Brownian motion.- B. The Ray—Knight description of local time.- C. The second formula of D. Williams.- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift.- 6.6. Solutions to Selected Problems.- 6.7. Notes.

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Book SynopsisThis is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus.Table of Contents1 Introduction.- 1.1 Equally Likely Outcomes.- 1.2 Interpretations.- 1.3 Distributions.- 1.4 Conditional Probability and Independence.- 1.5 Bayes’ Rule.- 1.6 Sequences of Events.- Summary.- Review Exercises.- 2 Repeated Trials and Sampling.- 2.1 The Binomial Distribution.- 2.2 Normal Approximation: Method.- 2.3 Normal Approximation: Derivation (Optional).- 2.4 Poisson Approximation.- 2.5 Random Sampling.- Summary.- Review Exercises.- 3 Random Variables.- 3.1 Introduction.- 3.2 Expectation.- 3.3 Standard Deviation and Normal Approximation.- 3.4 Discrete Distributions.- 3.5 The Poisson Distribution.- 3.6 Symmetry (Optional).- Summary.- Review Exercises.- 4 Continuous Distributions.- 4.1 Probability Densities.- 4.2 Exponential and Gamma Distributions.- 4.3 Hazard Rates (Optional).- 4.4 Change of Variable.- 4.5 Cumulative Distribution Functions.- 4.6 Order Statistics (Optional).- Summary.- Review Exercises.- 5 Continuous Joint Distributions.- 5.1 Uniform Distributions.- 5.2 Densities.- 5.3 Independent Normal Variables.- 5.4 Operations (Optional).- Summary.- Review Exercises.- 6 Dependence.- 6.1 Conditional Distributions: Discrete Case.- 6.2 Conditional Expectation: Discrete Case.- 6.3 Conditioning: Density Case.- 6.4 Covariance and Correlation.- 6.5 Bivariate Normal.- Summary.- Review Exercises.- Distribution Summaries.- Discrete.- Continuous.- Beta.- Binomial.- Exponential.- Gamma.- Geometric and Negative Binomial.- Hypergeometrie.- Normal.- Poisson.- Uniform.- Examinations.- Solutions to Examinations.- Appendices.- 1 Counting.- 2 Sums.- 3 Calculus.- 4 Exponents and Logarithms.- 5 Normal Table.- Brief Solutions to Odd-Numbered Exercises.

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Book SynopsisComputational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics.Trade ReviewFrom the reviews:“This is a book that covers many of the computational issues that statisticians will encounter as part of their research and applied work. … The writing in the book is quite clear and the author has done a good job providing the essence of each topic. … Overall, I think this is an excellent book. … This book will give a graduate student a good overview of the field. There are exercises provided for each chapter together with some solutions.” (Michael J. Evans, Mathematical Reviews, Issue 2011 b)“This book is a superior treatment of the important subject of statistical computing. I strongly recommend this book to anyone who analyzes data using either a commercial statistical software package or statistical computer programs written by the user or someone else. Thus this book is important not only for data oriented statisticians but for econometricians, psychometricians, political methodologists and biometricians as well. … All terms in this work including computing terms are clearly defined.” (Melvin Hinich, Technometrics, Vol. 53 (1), February, 2011)“I greatly appreciated the author’s command of both numerical and statistical computing … . The book also contains many exercises that substantiate the concepts, with solutions and hints in the appendix, an extensive bibliography, and a link to further literature and notes. The target readership includes undergraduates, postgraduates in statistics and allied fields such as computer science and mathematics, scientific research workers, and practitioners of statistics and numerical techniques. … I strongly recommend it for all scientific libraries.” (Soubhik Chakraborty, ACM Computing Reviews, October, 2010)“This book has a very large scope in that … it covers the dual fields of computational statistics and of statistical computing. … must-read for all students and researchers engaging into any kind of serious statistical programming. … is well-written, in a lively and personal style. … a reference book that should appear in the shortlist of any computational statistics/statistical computing graduate course as well as on the shelves of any researchers supporting his or her statistical practice with a significant dose of computing backup.”­­­ (Christian P. Robert, Statistical and Computation, Vol. 21, 2011)Table of ContentsPreliminaries.- Mathematical and Statistical Preliminaries.- Statistical Computing.- Computer Storage and Arithmetic.- Algorithms and Programming.- Approximation of Functions and Numerical Quadrature.- Numerical Linear Algebra.- Solution of Nonlinear Equations and Optimization.- Generation of Random Numbers.- Methods of Computational Statistics.- Graphical Methods in Computational Statistics.- Tools for Identification of Structure in Data.- Estimation of Functions.- Monte Carlo Methods for Statistical Inference.- Data Randomization, Partitioning, and Augmentation.- Bootstrap Methods.- Exploring Data Density and Relationships.- Estimation of Probability Density Functions Using Parametric Models.- Nonparametric Estimation of Probability Density Functions.- Statistical Learning and Data Mining.- Statistical Models of Dependencies.

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Book SynopsisIn the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case.Trade ReviewFrom the reviews: SIAM REVIEW "The presentation of this book is systematic and self-contained…Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) course…This book is highly recommended to anyone who wishes to study the relationship between Pontryagin’s maximum principle and Bellman’s dynamic programming principle applied to diffusion processes." MATHEMATICS REVIEW This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. ReviewTable of Contents1. Basic Stochastic Calculus.- 1. Probability.- 1.1. Probability spaces.- 1.2. Random variables.- 1.3. Conditional expectation.- 1.4. Convergence of probabilities.- 2. Stochastic Processes.- 2.1. General considerations.- 2.2. Brownian motions.- 3. Stopping Times.- 4. Martingales.- 5. Itô’s Integral.- 5.1. Nondifferentiability of Brownian motion.- 5.2. Definition of Itô’s integral and basic properties.- 5.3. Itô’s formula.- 5.4. Martingale representation theorems.- 6. Stochastic Differential Equations.- 6.1. Strong solutions.- 6.2. Weak solutions.- 6.3. Linear SDEs.- 6.4. Other types of SDEs.- 2. Stochastic Optimal Control Problems.- 1. Introduction.- 2. Deterministic Cases Revisited.- 3. Examples of Stochastic Control Problems.- 3.1. Production planning.- 3.2. Investment vs. consumption.- 3.3. Reinsurance and dividend management.- 3.4. Technology diffusion.- 3.5. Queueing systems in heavy traffic.- 4. Formulations of Stochastic Optimal Control Problems.- 4.1. Strong formulation.- 4.2. Weak formulation.- 5. Existence of Optimal Controls.- 5.1. A deterministic result.- 5.2. Existence under strong formulation.- 5.3. Existence under weak formulation.- 6. Reachable Sets of Stochastic Control Systems.- 6.1. Nonconvexity of the reachable sets.- 6.2. Noncloseness of the reachable sets.- 7. Other Stochastic Control Models.- 7.1. Random duration.- 7.2. Optimal stopping.- 7.3. Singular and impulse controls.- 7.4. Risk-sensitive controls.- 7.5. Ergodic controls.- 7.6. Partially observable systems.- 8. Historical Remarks.- 3. Maximum Principle and Stochastic Hamiltonian Systems.- 1. Introduction.- 2. The Deterministic Case Revisited.- 3. Statement of the Stochastic Maximum Principle.- 3.1. Adjoint equations.- 3.2. The maximum principle and stochastic Hamiltonian systems.- 3.3. A worked-out example.- 4. A Proof of the Maximum Principle.- 4.1. A moment estimate.- 4.2. Taylor expansions.- 4.3. Duality analysis and completion of the proof.- 5. Sufficient Conditions of Optimality.- 6. Problems with State Constraints.- 6.1. Formulation of the problem and the maximum principle.- 6.2. Some preliminary lemmas.- 6.3. A proof of Theorem 6.1.- 7. Historical Remarks.- 4. Dynamic Programming and HJB Equations.- 1. Introduction.- 2. The Deterministic Case Revisited.- 3. The Stochastic Principle of Optimality and the HJB Equation.- 3.1. A stochastic framework for dynamic programming.- 3.2. Principle of optimality.- 3.3. The HJB equation.- 4. Other Properties of the Value Function.- 4.1. Continuous dependence on parameters.- 4.2. Semiconcavity.- 5. Viscosity Solutions.- 5.1. Definitions.- 5.2. Some properties.- 6. Uniqueness of Viscosity Solutions.- 6.1. A uniqueness theorem.- 6.2. Proofs of Lemmas 6.6 and 6.7.- 7. Historical Remarks.- 5. The Relationship Between the Maximum Principle and Dynamic Programming.- 1. Introduction.- 2. Classical Hamilton-Jacobi Theory.- 3. Relationship for Deterministic Systems.- 3.1. Adjoint variable and value function: Smooth case.- 3.2. Economic interpretation.- 3.3. Methods of characteristics and the Feynman-Kac formula.- 3.4. Adjoint variable and value function: Nonsmooth case.- 3.5. Verification theorems.- 4. Relationship for Stochastic Systems.- 4.1. Smooth case.- 4.2. Nonsmooth case: Differentials in the spatial variable.- 4.3. Nonsmooth case: Differentials in the time variable.- 5. Stochastic Verification Theorems.- 5.1. Smooth case.- 5.2. Nonsmooth case.- 6. Optimal Feedback Controls.- 7. Historical Remarks.- 6. Linear Quadratic Optimal Control Problems.- 1. Introduction.- 2. The Deterministic LQ Problems Revisited.- 2.1. Formulation.- 2.2. A minimization problem of a quadratic functional.- 2.3. A linear Hamiltonian system.- 2.4. The Riccati equation and feedback optimal control.- 3. Formulation of Stochastic LQ Problems.- 3.1. Statement of the problems.- 3.2. Examples.- 4. Finiteness and Solvability.- 5. A Necessary Condition and a Hamiltonian System.- 6. Stochastic Riccati Equations.- 7. Global Solvability of Stochastic Riccati Equations.- 7.1. Existence: The standard case.- 7.2. Existence: The case C = 0, S = 0, and Q, G ?0.- 7.3. Existence: The one-dimensional case.- 8. A Mean-variance Portfolio Selection Problem.- 9. Historical Remarks.- 7. Backward Stochastic Differential Equations.- 1. Introduction.- 2. Linear Backward Stochastic Differential Equations.- 3. Nonlinear Backward Stochastic Differential Equations.- 3.1. BSDEs in finite deterministic durations: Method of contraction mapping.- 3.2. BSDEs in random durations: Method of continuation.- 4. Feynman—Kac-Type Formulae.- 4.1. Representation via SDEs.- 4.2. Representation via BSDEs.- 5. Forward—Backward Stochastic Differential Equations.- 5.1. General formulation and nonsolvability.- 5.2. The four-step scheme, a heuristic derivation.- 5.3. Several solvable classes of FBSDEs.- 6. Option Pricing Problems.- 6.1. European call options and the Black--Scholes formula.- 6.2. Other options.- 7. Historical Remarks.- References.

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Book SynopsisUncertainty, Intuition and Expectation.- Expectation.- Probability.- Some Basic Models.- Conditioning.- Applications of the Independence Concept.- The Two Basic Limit Theorems.- Continuous Random Variables and Their Transformations.- Markov Processes in Discrete Time.- Markov Processes in Continuous Time.- Action Optimisation: Dynamic Programming.- Optimal Resource Allocation.- Finance: Option Pricing and the Implied Martingale.- Second-Order Theory.- Consistency and Extension: The Finite-Dimensional Case.- Stochastic Convergence.- Martingales.- Extension: Examples of the Infinite-Dimensional Case.- Large-Deviation Theory.- Quantum Mechanics.Trade Review“This surprising and beautiful introduction to concepts of probability … chapters have been added which deal with areas of big actual interest … .” (Peter Imkeller, zbMATH 0980.60004, 2022)From the reviews of the fourth edition: "... a clear success in its unorthodoxy, Probability via Expectation has become a treasured classic."P.A.L. Emrechts in "Short Book Reviews", Vol. 21/1, April, 2001 "Apart from presenting a case for the development of probability theory by using the expectation operator rather than probability measure as the primitive notion, a second distinctive feature of this book is the very large range of modern applications that it covers. Many of these are addressed by more than 350 exercises interspersed throughout the text. In summary, this well written book is a … introduction to probability theory and its applications." (Norbert Henze, Metrika, November, 2002) "Originally published in 1970, this book has stood the test of time. … the text demonstrates a modern alternative approach to a now classical field. … The fourth edition contains a number of modifications and corrections. New material on dynamic programming, optimal allocation, options pricing and large deviations is included." (Martin T. Wells, Journal of the American Statistical Association, September 2001)Table of Contents1 Uncertainty, Intuition, and Expectation.- 1 Ideas and Examples.- 2 The Empirical Basis.- 3 Averages over a Finite Population.- 4 Repeated Sampling: Expectation.- 5 More on Sample Spaces and Variables.- 6 Ideal and Actual Experiments: Observables.- 2 Expectation.- 1 Random Variables.- 2 Axioms for the Expectation Operator.- 3 Events: Probability.- 4 Some Examples of an Expectation.- 5 Moments.- 6 Applications: Optimization Problems.- 7 Equiprobable Outcomes: Sample Surveys.- 8 Applications: Least Square Estimation of Random Variables.- 9 Some Implications of the Axioms.- 3 Probability.- 1 Events, Sets and Indicators.- 2 Probability Measure.- 3 Expectation as a Probability Integral.- 4 Some History.- 5 Subjective Probability.- 4 Some Basic Models.- 1 A Model of Spatial Distribution.- 2 The Multinomial, Binomial, Poisson and Geometric Distributions.- 3 Independence.- 4 Probability Generating Functions.- 5 The St. Petersburg Paradox.- 6 Matching, and Other Combinatorial Problems.- 7 Conditioning.- 8 Variables on the Continuum: The Exponential and Gamma Distributions.- 5 Conditioning.- 1 Conditional Expectation.- 2 Conditional Probability.- 3 A Conditional Expectation as a Random Variable.- 4 Conditioning on a ? Field.- 5 Independence.- 6 Statistical Decision Theory.- 7 Information Transmission.- 8 Acceptance Sampling.- 6 Applications of the Independence Concept.- 1 Renewal Processes.- 2 Recurrent Events: Regeneration Points.- 3 A Result in Statistical Mechanics: The Gibbs Distribution.- 4 Branching Processes.- 7 The Two Basic Limit Theorems.- 1 Convergence in Distribution (Weak Convergence).- 2 Properties of the Characteristic Function.- 3 The Law of Large Numbers.- 4 Normal Convergence (the Central Limit Theorem).- 5 The Normal Distribution.- 6 The Law of Large Numbers and the Evaluation of Channel Capacity.- 8 Continuous Random Variables and Their Transformations.- 1 Distributions with a Density.- 2 Functions of Random Variables.- 3 Conditional Densities.- 9 Markov Processes in Discrete Time.- 1 Stochastic Processes and the Markov Property.- 2 The Case of a Discrete State Space: The Kolmogorov Equations.- 3 Some Examples: Ruin, Survival and Runs.- 4 Birth and Death Processes: Detailed Balance.- 5 Some Examples We Should Like to Defer.- 6 Random Walks, Random Stopping and Ruin.- 7 Auguries of Martingales.- 8 Recurrence and Equilibrium.- 9 Recurrence and Dimension.- 10 Markov Processes in Continuous Time.- 1 The Markov Property in Continuous Time.- 2 The Case of a Discrete State Space.- 3 The Poisson Process.- 4 Birth and Death Processes.- 5 Processes on Nondiscrete State Spaces.- 6 The Filing Problem.- 7 Some Continuous-Time Martingales.- 8 Stationarity and Reversibility.- 9 The Ehrenfest Model.- 10 Processes of Independent Increments.- 11 Brownian Motion: Diffusion Processes.- 12 First Passage and Recurrence for Brownian Motion.- 11 Action Optimisation; Dynamic Programming.- 1 Action Optimisation.- 2 Optimisation over Time: the Dynamic Programming Equation.- 3 State Structure.- 4 Optimal Control Under LQG Assumptions.- 5 Minimal-Length Coding.- 6 Discounting.- 7 Continuous-Time Versions and Infinite-Horizon Limits.- 8 Policy Improvement.- 12 Optimal Resource Allocation.- 1 Portfolio Selection in Discrete Time.- 2 Portfolio Selection in Continuous Time.- 3 Multi-Armed Bandits and the Gittins Index.- 4 Open Processes.- 5 Tax Problems.- 13 Finance: ‘Risk-Free’ Trading and Option Pricing.- 1 Options and Hedging Strategies.- 2 Optimal Targeting of the Contract.- 3 An Example.- 4 A Continuous-Time Model.- 5 How Should it Be Done?.- 14 Second-Order Theory.- 1 Back to L2.- 2 Linear Least Square Approximation.- 3 Projection: Innovation.- 4 The Gauss-Markov Theorem.- 5 The Convergence of Linear Least Square Estimates.- 6 Direct and Mutual Mean Square Convergence.- 7 Conditional Expectations as Least Square Estimates: Martingale Convergence.- 15 Consistency and Extension: The Finite-Dimensional Case.- 1 The Issues.- 2 Convex Sets.- 3 The Consistency Condition for Expectation Values.- 4 The Extension of Expectation Values.- 5 Examples of Extension.- 6 Dependence Information: Chernoff Bounds.- 16 Stochastic Convergence.- 1 The Characterization of Convergence.- 2 Types of Convergence.- 3 Some Consequences.- 4 Convergence in rth Mean.- 17 Martingales.- 1 The Martingale Property.- 2 Kolmogorov’s Inequality: the Law of Large Numbers.- 3 Martingale Convergence: Applications.- 4 The Optional Stopping Theorem.- 5 Examples of Stopped Martingales.- 18 Large-Deviation Theory.- 1 The Large-Deviation Property.- 2 Some Preliminaries.- 3 Cramer’s Theorem.- 4 Some Special Cases.- 5 Circuit-Switched Networks and Boltzmarm Statistics.- 6 Multi-Class Traffic and Effective Bandwidth.- 7 Birth and Death Processes.- 19 Extension: Examples of the Infinite-Dimensional Case.- 1 Generalities on the Infinite-Dimensional Case.- 2 Fields and ?-Fields of Events.- 3 Extension on a Linear Lattice.- 4 Integrable Functions of a Scalar Random Variable.- 5 Expectations Derivable from the Characteristic Function: Weak Convergence324.- 20 Quantum Mechanics.- 1 The Static Case.- 2 The Dynamic Case.- References.

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Book SynopsisLinear 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.Table of ContentsPreface. Notation and symbols. 1 Introduction. 1.1 Historical perspective. 1.2 How to use this book. 1.3 Outline of this book. 1.4 Notes and references. 2 Linear algebra. 2.1 Basic concepts in linear algebra. 2.2 Eigenvalues and eigenvectors. 2.3 Complex eigenvalues. 2.4 Cayley–Hamilton theorem. 2.5 Invariant subspaces and Jordan canonical form. 2.6 Semi-definite matrices. 2.7 Algebraic Riccati equations. 2.8 Notes and references. 2.9 Exercises. 2.10 Appendix. 3 Dynamical systems. 3.1 Description of linear dynamical systems. 3.2 Existence–uniqueness results for differential equations. 3.2.1 General case. 3.2.2 Control theoretic extensions. 3.3 Stability theory: general case. 3.4 Stability theory of planar systems. 3.5 Geometric concepts. 3.6 Performance specifications. 3.7 Examples of differential games. 3.8 Information, commitment and strategies. 3.9 Notes and references. 3.10 Exercises. 3.11 Appendix. 4 Optimization techniques. 4.1 Optimization of functions. 4.2 The Euler–Lagrange equation. 4.3 Pontryagin’s maximum principle. 4.4 Dynamic programming principle. 4.5 Solving optimal control problems. 4.6 Notes and references. 4.7 Exercises. 4.8 Appendix. 5 Regular linear quadratic optimal control. 5.1 Problem statement. 5.2 Finite-planning horizon. 5.3 Riccati differential equations. 5.4 Infinite-planning horizon. 5.5 Convergence results. 5.6 Notes and references. 5.7 Exercises. 5.8 Appendix. 6 Cooperative games. 6.1 Pareto solutions. 6.2 Bargaining concepts. 6.3 Nash bargaining solution. 6.4 Numerical solution. 6.5 Notes and references. 6.6 Exercises. 6.7 Appendix. 7 Non-cooperative open-loop information games. 7.1 Introduction. 7.2 Finite-planning horizon. 7.3 Open-loop Nash algebraic Riccati equations. 7.4 Infinite-planning horizon. 7.5 Computational aspects and illustrative examples. 7.6 Convergence results. 7.7 Scalar case. 7.8 Economics examples. 7.8.1 A simple government debt stabilization game. 7.8.2 A game on dynamic duopolistic competition. 7.9 Notes and references. 7.10 Exercises. 7.11 Appendix. 8 Non-cooperative feedback information games. 8.1 Introduction. 8.2 Finite-planning horizon. 8.3 Infinite-planning horizon. 8.4 Two-player scalar case. 8.5 Computational aspects. 8.5.1 Preliminaries. 8.5.2 A scalar numerical algorithm: the two-player case. 8.5.3 The N-player scalar case. 8.6 Convergence results for the two-player scalar case. 8.7 Notes and references. 8.8 Exercises. 8.9 Appendix. 9 Uncertain non-cooperative feedback information games. 9.1 Stochastic approach. 9.2 Deterministic approach: introduction. 9.3 The one-player case. 9.4 The one-player scalar case. 9.5 The two-player case. 9.6 A fishery management game. 9.7 A scalar numerical algorithm. 9.8 Stochastic interpretation. 9.9 Notes and references. 9.10 Exercises. 9.11 Appendix. References. Index.

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Book SynopsisModeling Random Processes for Engineers and Managers 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. Modeling Random Processes 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.Table of ContentsPreface ix 1 Probability Review 1 1.1 Interpreting and Using Probabilities 2 1.2 Sample Spaces and Events 3 1.3 Probability 4 1.4 Random Variables 6 1.5 Probability Distributions 6 1.6 Joint, Marginal, and Conditional Distributions 11 1.7 Expectation 14 1.8 Variance and Other Moments 16 1.9 The Law of Total Probability 18 1.10 Discrete Probability Distributions 20 1.11 Continuous Probability Distributions 23 1.12 Where Do Distributions Come From? 26 1.13 The Binomial Process 28 1.14 Recommended Reading 29 2 Formulating Markov Chain Models 32 2.1 An Example 33 2.2 Modeling the Progress of Time 34 2.3 Modeling Possibilities as States 36 2.4 Simplifying Assumptions 38 2.5 Modeling Changes of State as Transitions 40 2.6 Obtaining the Data 45 2.7 Another Example 46 2.8 A Case Study 47 2.9 Higher Order Markov Chains 50 2.10 Reducing the Number of States 52 2.11 Nonstationary Markov Chains 53 2.12 Other Example 54 2.13 Summary 67 2.14 Recommended Reading 67 3 Markov Chain Calculations 72 3.1 Walk Probabilities 73 3.2 Transition Probabilities 74 3.3 State Probabilities 78 3.4 A Numerical Example 79 3.5 Expected Number of Visits 80 3.6 Sojourn Times 82 3.7 First Passage and Return Probabilities 83 3.8 Computational Formulas for All Markov Chains 86 3.9 Special Classes of Markov Chains 86 3.10 Steady-State Probabilities 87 3.11 The Uses of Steady-State Results 92 3.12 Mean First Passage Times 93 3.13 Computational Formulas for Ergodic Markov Chains 96 3.14 Terminating Markov Chains 96 3.15 Expected Number of Visits 98 3.16 Expected Duration of a Terminating Process 99 3.17 Absorption Probabilities 100 3.18 Hit Probabilities 102 3.19 Conditional Mean First Passage Times to Absorbing States 103 3.20 Computational Formulas for Terminating Processes 105 3.21 Call Center Calculations 105 3.22 Classification Terminology 106 3.23 Additional Complications in Infinite Chains 111 3.24 Dealing with a Reducible Process 112 3.25 Periodic Chains 113 3.26 Ergodic Chains 114 3.27 Recommended Reading 115 4 Rewards on Markov Chains 119 4.1 Formulation 120 4.2 A Numerical Example 120 4.3 Expected Total Reward 121 4.4 Random Variable Rewards 124 4.5 Semi-Markov Processes 126 4.6 Limiting Results for Ergodic Processes 126 4.7 Total Reward for Terminating Processes 130 4.8 Case Study 132 4.9 Discounting 133 4.10 Case Study 135 4.11 Recommended Reading 137 5 Continuous Time Markov Processes 140 5.1 An Example 141 5.2 Interpreting Transition Rates 146 5.3 The Assumptions Reconsidered 149 5.4 Aging Does Not Affect the Transition Time 150 5.5 Competing Transitions 152 5.6 Sojourn Times 153 5.7 Embedded Markov Chains 154 5.8 Deriving the Differential Equations 155 5.9 Solving the Differential Equations 157 5.10 State Probabilities 159 5.11 First Passage Probability Functions 159 5.12 State Classification 160 5.13 Steady-State Probabilities 161 5.14 Other Computable Quantities 163 5.15 Case Study 165 5.16 Birth-Death Processes 167 5.17 The Poisson Process 169 5.18 Properties of Poisson Processes 171 5.19 Khintchine’s Theorem 172 5.20 Phase-Type Distributions 173 5.21 Conclusions 175 5.22 Recommended Reading 175 6 Queueing Models 179 6.1 An Example 180 6.2 General Characteristics 182 6.3 Performance Measures 186 6.4 Relations Among Performance Measures 188 6.5 Little’s Formula 190 6.6 Markovian Queueing Models 191 6.7 The M/M/1 Model 193 6.8 The Significance of Traffic Intensity 198 6.9 Unnormalized Solutions 200 6.10 Limited Queue Capacity 202 6.11 Multiple Servers 204 6.12 Is It Better to Merge or Separate Servers? 207 6.13 Which is Better: More Servers or Faster Servers 208 6.14 Case Study: A Grain Elevator 209 6.15 The M/M/c/c and M/M/1 Models 210 6.16 Finite Sources 212 6.17 The Machine Repairmen Model 214 6.18 Numerical Calculations Using a Spreadsheet 214 6.19 Queue Discipline Variations 217 6.20 Non-Markovian Queues 218 6.21 The M/G/1 Model 219 6.22 Approximate Solutions for Other Models 220 6.23 Conclusion 221 6.24 Recommended Reading 221 7 Networks of Queues 225 7.1 Open Networks of Markovian Queues 226 7.2 An Example Open Network 227 7.3 Extensions 228 7.4 Closed Networks 229 7.5 A Preliminary Example 229 7.6 Relative Arrival Rates 230 7.7 Unnormalized Solutions for Individual Stations 232 7.8 Assembling the Pieces of the Solution 234 7.9 Calculating the Normalization Constant 235 7.10 Performance Measures for Closed Networks 237 7.11 Creating a Closed Model 239 7.12 Case Study 242 7.13 Extensions 247 7.14 Approximate Methods 247 7.15 Recommended Reading 248 8 Using the Transition Diagram to Compute 251 8.1 An Example 252 8.2 Definitions 254 8.3 Steady-State Probabilities 258 8.4 How to Generate All In-trees 259 8.5 Check Your Understanding 262 8.6 Generalization to Other Quantities 263 8.7 Mean First Passage Times 264 8.8 Results for Terminating Processes 265 8.9 How to Simplify the Arithmetic 266 8.10 How to Systematically Generate r-Forests 267 8.11 Summary of Results 267 8.12 How to Remember the Formulas 268 8.13 Advanced Topics 268 8.14 Recommended Reading 269 Appendix 1 271 Appendix 2 278 Index 300

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Book SynopsisAn 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.Table of ContentsForeword to the first edition xiii From the preface to the first edition xvii Preface to the second edition xix Preface to the third edition xxi Notation xxiii 1 Mathematical foundations 1 1.1 Set theory 1 1.2 Topology in Euclidean spaces 3 1.3 Operations on subsets of Euclidean space 5 1.4 Mathematical morphology and image analysis 7 1.5 Euclidean isometries 9 1.6 Convex sets in Euclidean spaces 10 1.7 Functions describing convex sets 17 1.8 Polyconvex sets 24 1.9 Measure and integration theory 27 2 Point processes I: The Poisson point process 35 2.1 Introduction 35 2.2 The binomial point process 36 2.3 The homogeneous Poisson point process 41 2.4 The inhomogeneous and general Poisson point process 51 2.5 Simulation of Poisson point processes 53 2.6 Statistics for the homogeneous Poisson point process 55 3 Random closed sets I: The Boolean model 64 3.1 Introduction and basic properties 64 3.2 The Boolean model with convex grains 78 3.3 Coverage and connectivity 89 3.4 Statistics 95 3.5 Generalisations and variations 103 3.6 Hints for practical applications 106 4 Point processes II: General theory 108 4.1 Basic properties 108 4.2 Marked point processes 116 4.3 Moment measures and related quantities 120 4.4 Palm distributions 127 4.5 The second moment measure 139 4.6 Summary characteristics 143 4.7 Introduction to statistics for stationary spatial point processes 145 4.8 General point processes 156 5 Point processes III: Models 158 5.1 Operations on point processes 158 5.2 Doubly stochastic Poisson processes (Cox processes) 166 5.3 Neyman–Scott processes 171 5.4 Hard-core point processes 176 5.5 Gibbs point processes 178 5.6 Shot-noise fields 200 6 Random closed sets II: The general case 205 6.1 Basic properties 205 6.2 Random compact sets 213 6.3 Characteristics for stationary and isotropic random closed sets 216 6.4 Nonparametric statistics for stationary random closed sets 230 6.5 Germ–grain models 237 6.6 Other random closed set models 255 6.7 Stochastic reconstruction of random sets 276 7 Random measures 279 7.1 Fundamentals 279 7.2 Moment measures and related characteristics 284 7.3 Examples of random measures 286 8 Line, fibre and surface processes 297 8.1 Introduction 297 8.2 Flat processes 302 8.3 Planar fibre processes 314 8.4 Spatial fibre processes 330 8.5 Surface processes 333 8.6 Marked fibre and surface processes 339 9 Random tessellations, geometrical networks and graphs 343 9.1 Introduction and definitions 343 9.2 Mathematical models for random tessellations 346 9.3 General ideas and results for stationary planar tessellations 357 9.4 Mean-value formulae for stationary spatial tessellations 367 9.5 Poisson line and plane tessellations 370 9.6 STIT tessellations 375 9.7 Poisson-Voronoi and Delaunay tessellations 376 9.8 Laguerre tessellations 386 9.9 Johnson–Mehl tessellations 388 9.10 Statistics for stationary tessellations 390 9.11 Random geometrical networks 397 9.12 Random graphs 402 10 Stereology 411 10.1 Introduction 411 10.2 The fundamental mean-value formulae of stereology 413 10.3 Stereological mean-value formulae for germ–grain models 421 10.4 Stereological methods for spatial systems of balls 425 10.5 Stereological problems for nonspherical grains (shape-and-size problems) 436 10.6 Stereology for spatial tessellations 440 10.7 Second-order characteristics and directional distributions 444 References 453 Author index 507 Subject index 521

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Book SynopsisCovers 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.Table of ContentsPreface xi Acknowledgement xiii 1 Introduction and Notation 1 1.1 Claims process 1 1.1.1 Accounting principles and accident years 2 1.1.2 Inflation 3 1.2 Structural framework to the claims-reserving problem 5 1.2.1 Fundamental properties of the claims reserving process 7 1.2.2 Known and unknown claims 9 1.3 Outstanding loss liabilities, classical notation 10 1.4 General remarks 12 2 Basic Methods 15 2.1 Chain-ladder method (distribution-free) 15 2.2 Bornhuetter–Ferguson method 21 2.3 Number of IBNyR claims, Poisson model 25 2.4 Poisson derivation of the CL algorithm 27 3 Chain-Ladder Models 33 3.1 Mean square error of prediction 33 3.2 Chain-ladder method 36 3.2.1 Mack model (distribution-free CL model) 37 3.2.2 Conditional process variance 41 3.2.3 Estimation error for single accident years 44 3.2.4 Conditional MSEP, aggregated accident years 55 3.3 Bounds in the unconditional approach 58 3.3.1 Results and interpretation 58 3.3.2 Aggregation of accident years 63 3.3.3 Proof of Theorems 3.17, 3.18 and 3.20 64 3.4 Analysis of error terms in the CL method 70 3.4.1 Classical CL model 70 3.4.2 Enhanced CL model 71 3.4.3 Interpretation 72 3.4.4 CL estimator in the enhanced model 73 3.4.5 Conditional process and parameter prediction errors 74 3.4.6 CL factors and parameter estimation error 75 3.4.7 Parameter estimation 81 4 Bayesian Models 91 4.1 Benktander–Hovinen method and Cape–Cod model 91 4.1.1 Benktander–Hovinen method 92 4.1.2 Cape–Cod model 95 4.2 Credible claims reserving methods 98 4.2.1 Minimizing quadratic loss functions 98 4.2.2 Distributional examples to credible claims reserving 101 4.2.3 Log-normal/Log-normal model 105 4.3 Exact Bayesian models 113 4.3.1 Overdispersed Poisson model with gamma prior distribution 114 4.3.2 Exponential dispersion family with its associated conjugates 122 4.4 Markov chain Monte Carlo methods 131 4.5 Bühlmann–Straub credibility model 145 4.6 Multidimensional credibility models 154 4.6.1 Hachemeister regression model 155 4.6.2 Other credibility models 159 4.7 Kalman filter 160 5 Distributional Models 167 5.1 Log-normal model for cumulative claims 167 5.1.1 Known variances σj 2 170 5.1.2 Unknown variances 177 5.2 Incremental claims 182 5.2.1 (Overdispersed) Poisson model 182 5.2.2 Negative-Binomial model 183 5.2.3 Log-normal model for incremental claims 185 5.2.4 Gamma model 186 5.2.5 Tweedie’s compound Poisson model 188 5.2.6 Wright’s model 199 6 Generalized Linear Models 201 6.1 Maximum likelihood estimators 201 6.2 Generalized linear models framework 203 6.3 Exponential dispersion family 205 6.4 Parameter estimation in the EDF 208 6.4.1 MLE for the EDF 208 6.4.2 Fisher’s scoring method 210 6.4.3 Mean square error of prediction 214 6.5 Other GLM models 223 6.6 Bornhuetter–Ferguson method, revisited 223 6.6.1 MSEP in the BF method, single accident year 226 6.6.2 MSEP in the BF method, aggregated accident years 230 7 Bootstrap Methods 233 7.1 Introduction 233 7.1.1 Efron’s non-parametric bootstrap 234 7.1.2 Parametric bootstrap 236 7.2 Log-normal model for cumulative sizes 237 7.3 Generalized linear models 242 7.4 Chain-ladder method 244 7.4.1 Approach 1: Unconditional estimation error 246 7.4.2 Approach 3: Conditional estimation error 247 7.5 Mathematical thoughts about bootstrapping methods 248 7.6 Synchronous bootstrapping of seemingly unrelated regressions 253 8 Multivariate Reserving Methods 257 8.1 General multivariate framework 257 8.2 Multivariate chain-ladder method 259 8.2.1 Multivariate CL model 259 8.2.2 Conditional process variance 264 8.2.3 Conditional estimation error for single accident years 265 8.2.4 Conditional MSEP, aggregated accident years 272 8.2.5 Parameter estimation 274 8.3 Multivariate additive loss reserving method 288 8.3.1 Multivariate additive loss reserving model 288 8.3.2 Conditional process variance 295 8.3.3 Conditional estimation error for single accident years 295 8.3.4 Conditional MSEP, aggregated accident years 297 8.3.5 Parameter estimation 299 8.4 Combined Multivariate CL and ALR method 308 8.4.1 Combined CL and ALR method: the model 308 8.4.2 Conditional cross process variance 313 8.4.3 Conditional cross estimation error for single accident years 315 8.4.4 Conditional MSEP, aggregated accident years 319 8.4.5 Parameter estimation 321 9 Selected Topics I: Chain-Ladder Methods 331 9.1 Munich chain-ladder 331 9.1.1 The Munich chain-ladder model 333 9.1.2 Credibility approach to the MCL method 335 9.1.3 MCL Parameter estimation 340 9.2 CL Reserving: A Bayesian inference model 346 9.2.1 Prediction of the ultimate claim 351 9.2.2 Likelihood function and posterior distribution 351 9.2.3 Mean square error of prediction 354 9.2.4 Credibility chain-ladder 359 9.2.5 Examples 361 9.2.6 Markov chain Monte Carlo methods 364 10 Selected Topics II: Individual Claims Development Processes 369 10.1 Modelling claims development processes for individual claims 369 10.1.1 Modelling framework 370 10.1.2 Claims reserving categories 376 10.2 Separating IBNeR and IBNyR claims 379 11 Statistical Diagnostics 391 11.1 Testing age-to-age factors 391 11.1.1 Model choice 394 11.1.2 Age-to-age factors 396 11.1.3 Homogeneity in time and distributional assumptions 398 11.1.4 Correlations 399 11.1.5 Diagonal effects 401 11.2 Non-parametric smoothing 401 Appendix A: Distributions 405 A.1 Discrete distributions 405 A.1.1 Binomial distribution 405 A.1.2 Poisson distribution 405 A.1.3 Negative-Binomial distribution 405 A.2 Continuous distributions 406 A.2.1 Uniform distribution 406 A.2.2 Normal distribution 406 A.2.3 Log-normal distribution 407 A.2.4 Gamma distribution 407 A.2.5 Beta distribution 408 Bibliography 409 Index 417

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Book SynopsisLevy 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.Trade Review"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." (Zentralblatt MATH, 2010) Table of ContentsPreface. Acknowledgements. PART I: INTRODUCTION. 1 An Introduction to Credit Risk. 1.1 Credit Risk. 1.1.1 Historical and Risk-Neutral Probabilities. 1.1.2 Bond Prices and Default Probability. 1.2 Credit Risk Modelling. 1.3 Credit Derivatives. 1.4 Modelling Assumptions. 1.4.1 Probability Space and Filtrations. 1.4.2 The Risk-Free Asset. 2 An Introduction to Lévy Processes. 2.1 Brownian Motion. 2.2 Lévy Processes. 2.3 Examples of Lévy Processes. 2.3.1 Poisson Process. 2.3.2 Compound Poisson Process. 2.3.3 The Gamma Process. 2.3.4 Inverse Gaussian Process. 2.3.5 The CMY Process. 2.3.6 The Variance Gamma Process. 2.4 Ornstein–Uhlenbeck Processes. 2.4.1 The Gamma-OU Process. 2.4.2 The Inverse Gaussian-OU Process. PART II: SINGLE-NAME MODELLING. 3 Single-Name Credit Derivatives. 3.1 Credit Default Swaps. 3.1.1 Credit Default Swaps Pricing. 3.1.2 Calibration Assumptions. 3.2 Credit Default Swap Forwards. 3.2.1 Credit Default Swap Forward Pricing. 3.3 Constant Maturity Credit Default Swaps. 3.3.1 Constant Maturity Credit Default Swaps Pricing. 3.4 Options on CDS. 4 Firm-Value Lévy Models. 4.1 The Merton Model. 4.2 The Black–Cox Model with Constant Barrier. 4.3 The Lévy First-Passage Model. 4.4 The Variance Gamma Model. 4.4.1 Sensitivity to the Parameters. 4.4.2 Calibration on CDS Term Structure Curve. 4.5 One-Sided Lévy Default Model. 4.5.1 Wiener–Hopf Factorization and Default Probabilities. 4.5.2 Illustration of the Pricing of Credit Default Swaps. 4.6 Dynamic Spread Generator. 4.6.1 Generating Spread Paths. 4.6.2 Pricing of Options on CDSs. 4.6.3 Black’s Formulas and Implied Volatility. Appendix: Solution of the PDIE. 5 IntensityLévy Models. 5.1 Intensity Models for Credit Risk. 5.1.1 Jarrow–Turnbull Model. 5.1.2 Cox Models. 5.2 The Intensity-OU Model. 5.3 Calibration of the Model on CDS Term Structures. PART III: MULTIVARIATE MODELLING. 6 Multivariate Credit Products. 6.1 CDOs. 6.2 Credit Indices. 7 Collateralized Debt Obligations. 7.1 Introduction. 7.2 The Gaussian One-Factor Model. 7.3 Generic One-Factor Lévy Model. 7.4 Examples of Lévy Models. 7.5 Lévy Base Correlation. 7.5.1 The Concept of Base Correlation. 7.5.2 Pricing Non-Standard Tranches. 7.5.3 Correlation Mapping for Bespoke CDOs. 7.6 Delta-Hedging CDO tranches. 7.6.1 Hedging with the CDS Index. 7.6.2 Delta-Hedging with a Single-Name CDS. 7.6.3 Mezz-Equity hedging. 8 Multivariate Index Modelling. 8.1 Black’s Model. 8.2 VG Credit Spread Model. 8.3 Pricing Swaptions using FFT. 8.4 Multivariate VG Model. PART IV: EXOTIC STRUCTURED CREDIT RISK PRODUCTS. 9 Credit CPPIs and CPDOs. 9.1 Introduction. 9.2 CPPIs. 9.3 Gap Risk. 9.4 CPDOs. 10 Asset-Backed Securities. 10.1 Introduction. 10.2 Default Models. 10.2.1 Generalized Logistic Default Model. 10.2.2 Lévy Portfolio Default Model. 10.2.3 Normal One-Factor Default Model. 10.2.4 Generic One-Factor Lévy Default Model. 10.3 Prepayment Models. 10.3.1 Constant Prepayment Model. 10.3.2 Lévy Portfolio Prepayment Model. 10.3.3 Normal One-Factor Prepayment Model. 10.4 Numerical Results. Bibliography. Index.

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Book SynopsisPraise for the First Edition . . . an excellent textbook . . . well organized and neatly written. Mathematical Reviews . . . amazingly interesting . . . Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning 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 statiTable of ContentsPreface xi Preface to the First Edition xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15 1.4.1 Combinatorics 17 1.5 Conditional Probability and Independence 27 1.6 The Law of Total Probability and Bayes’ Formula 41 Problems 63 2 Random Variables 76 2.1 Introduction 76 2.2 Discrete Random Variables 77 2.3 Continuous Random Variables 82 2.4 Expected Value and Variance 95 2.5 Special Discrete Distributions 111 2.6 The Exponential Distribution 123 2.7 The Normal Distribution 127 2.8 Other Distributions 131 2.9 Location Parameters 137 2.10 The Failure Rate Function 139 Problems 144 3 Joint Distributions 156 3.1 Introduction 156 3.2 The Joint Distribution Function 156 3.3 Discrete Random Vectors 158 3.4 Jointly Continuous Random Vectors 160 3.5 Conditional Distributions and Independence 164 3.5.1 Independent Random Variables 168 3.6 Functions of Random Vectors 172 3.7 Conditional Expectation 185 3.8 Covariance and Correlation 196 3.9 The Bivariate Normal Distribution 209 3.10 Multidimensional Random Vectors 216 3.11 Generating Functions 231 3.12 The Poisson Process 240 Problems 247 4 Limit Theorems 263 4.1 Introduction 263 4.2 The Law of Large Numbers 264 4.3 The Central Limit Theorem 268 4.4 Convergence in Distribution 275 Problems 278 5 Simulation 281 5.1 Introduction 281 5.2 Random Number Generation 282 5.3 Simulation of Discrete Distributions 283 5.4 Simulation of Continuous Distributions 285 5.5 Miscellaneous 290 Problems 292 6 Statistical Inference 294 6.1 Introduction 294 6.2 Point Estimators 294 6.3 Confidence Intervals 304 6.4 Estimation Methods 312 6.5 Hypothesis Testing 327 6.6 Further Topics in Hypothesis Testing 334 6.7 Goodness of Fit 339 6.8 Bayesian Statistics 351 6.9 Nonparametric Methods 363 Problems 378 7 Linear Models 391 7.1 Introduction 391 7.2 Sampling Distributions 392 7.3 Single Sample Inference 395 7.4 Comparing Two Samples 402 7.5 Analysis of Variance 409 7.6 Linear Regression 415 7.7 The General Linear Model 431 Problems 436 8 Stochastic Processes 444 8.1 Introduction 444 8.2 Discrete -Time Markov Chains 445 8.3 Random Walks and Branching Processes 464 8.4 Continuous -Time Markov Chains 475 8.5 Martingales 494 8.6 Renewal Processes 502 8.7 Brownian Motion 509 Problems 517 Appendix A Tables 527 Appendix B Answers to Selected Problems 535 Further Reading 551 Index 553

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Book SynopsisMethods 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.Trade Review"...has a merit for everyone who wonders about the foundations ofinference..." (Australian & New Zealand J Statistics, 2000)Table of ContentsPhilosophical and Historical Introduction. Quantities, Prevision, and Coherency. Coherent Statistical Inference. Related Forms for Asserting Uncertain Knowledge. Distribution Functions. Proper Scoring Rules. The Multivariate Normal Distribution and Its Mixtures. Sequential Forecasting Based on Linear Conditional PrevisionStructures: Theory and Practice of Linear Regression. The Direction of Statistical Research. References. Index.

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Book SynopsisThis 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.Trade Review“This new edition of a successful, bestselling book continues to provide you with practical information on the useof statistical methods for solving real-world problems in complex industrial environments.” (PDFCHM Online, 27 February 2013) "...a comprehensive, very useful and clear guide for all analytical chemists..." (Annali di Chimica, Vol 153, 2000) "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) "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)Table of ContentsUnivariate Data. Bi- and Multivariate Data. Related Topics. Complex Examples. Appendices. Technical Tidbits. Glossary. References. Index.

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Book SynopsisThis 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.Table of ContentsPreliminaries. Computation of Expectations in Finite Dimension. Simulation of Random Processes. Deterministic Resolution of Some Markovian Problems. Stochastic Differential Equations and Brownian Functionals. Notes. References. Index.

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Book SynopsisThe 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. [A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference. -American Scientist 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. -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference wTable of ContentsIntroduction. 1. Operator Semigroups. 2. Stochastic Processes and Martingales. 3. Convergence of Probability Measures. 4. Generators and Markov Processes. 5. Stochastic Integral Equations. 6. Random Time Changes. 7. Invariance Principles and Diffusion Approximations. 8. Examples of Generators. 9. Branching Processes. 10. Genetic Models. 11. Density Dependent Population Processes. 12. Random Evolutions. Appendixes. References. Index. Flowchart.

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