Stochastics Books
Springer International Publishing AG Marginal and Functional Quantization of
Book SynopsisVector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.Table of ContentsPreface.- Notation Index.- Part I. Basics and Marginal Quantization.- 1. Optimal and Stationary Quantizers.- 2. The Finite-Dimensional Setting I.- 3. The Finite-Dimensional Setting II.- Part II. Functional Quantization.- 4. Functional Quantization, Small Ball Probabilities, Metric Entropy and Series Expansions for Gaussian Processes.- 5. Spectral Methods for Gaussian Processes.- 6. Geometry of Optimal and Rate-Optimal Quantizers for Gaussian Processes.- 7. Mean Regular Processes.- Part III. Algorithmic Aspects and Applications:- 8. Optimal Quantization from the Numerical Side (Static).- 9. Applications: Quantization-Based Cubature Formulas.- 10. Quantization-Based Numerical Schemes.- Appendices.- A. Radon Random Vectors, Stochastic Processes and Inequalities.- B. Miscellany.- References.- Index.
£999.99
Aarhus University Press Stochastic Dynamics
Book SynopsisIn chapter 1, the basic assumptions of the random vibration theory are emphasized. In chapters 2 and 3, pertinent results of stochastic variables and stochastic processes have been indicated. Chapter 4 deals with the stochastic response analysis of single degrees-of-freedom, multi-degrees-of-freedom and continuous linear structural systems. In principle, an introductory course on linear structural dynamics is presupposes. However, in order to make this textbook self-contained, short reviews of the most important results of linear deterministic vibration theory have been included in the start of the relevant sub-sections. Chapter 5 outlines the reliability theory for dynamically excited building structures, i.e., reliability theory for narrowbanded response processes. Finally, Chapter 6 gives an introduction to Monte Carlo simulation methods, which become increasingly important and useful as the computers become more and more powerful.
£18.95
Springer-Verlag New York Inc. Probability2
Book SynopsisThis third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.Trade Review“I think this would be an excellent text by itself for an advanced course in probability.” (Allen Stenger, MAA Reviews, October 26, 2019)Table of ContentsPreface.- Chapter 4: Sequences and Sums of Independent Random Variables.- Chapter 5: Stationary (Strict Sense) Random Sequences and Ergodic Theory.- Chapter 6: Stationary (Wide Sense) Random Sequences: L2-Theory.- Chapter 7: Martingales.- Chapter 8: Markov Chains.- Historical of Bibliographical Notes (Chapters 4-8).- References.- Index.- Index of Symbols.
£58.49
Springer The Pleasures of Probability
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.
£999.99
MP-AMM American Mathematical Probability Theory
Book SynopsisThis volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including all the standard topics.Table of ContentsMeasure theory; Weak convergence; Independent sums; Dependent random variables; Martingales; Stationary stochastic processes; Dynamic programming and filtering; Bibliography; Index
£25.60
MP-AMM American Mathematical The Shoelace Book A Mathematical Guide to the
Book SynopsisCrisscross, zigzag, bowtie, devil, angel, or star: which are the longest, the shortest, the strongest, and the weakest lacings? This book presents the mathematics of shoelaces which is a mix of combinatorics and elementary calculus.Table of ContentsSetting the stage One-column lacings Counting lacings The shortest lacings Variations on the shortest lacing problem The longest lacings The strongest lacings The weakest lacings Related mathematics Loose ends References Index.
£40.80
MP-AMM American Mathematical Complex Graphs and Networks
Book SynopsisBased on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, this work presents fresh perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate the information age.Table of ContentsGraph theory in the information age Old and new concentration inequalities A generative model--the preferential attachment scheme Duplication models for biological networks Random graphs with given expected degrees The rise of the giant component Average distance and the diameter Eigenvalues of the adjacency matrix of $G(\mathbf{w})$ The semi-circle law for $G(\mathbf{w})$ Coupling on-line and off-line analyses of random graphs The configuration model for power law graphs The small world phenomenon in hybrid graphs Bibliography Index.
£49.50
MP-AMM American Mathematical Advances in Stochastic Inequalities
Book SynopsisContains 15 articles based on invited talks given at an AMS Special Session on 'Stochastic Inequalities and Their Applications' held at Georgia Institute of Technology (Atlanta). This book includes articles that offer a comprehensive picture of this area of mathematical probability and statistics.Table of ContentsBounds on the non-convexity of ranges of vector measures with atoms by P. C. Allaart The class of Gaussian chaos of order two is closed by taking limits in distribution by M. A. Arcones Two inequalities and some applications in connection with $\rho*$-mixing, a survey by R. C. Bradley Variance inequalities for functions of multivariate random variables by W.-Y. Chang and D. St. P. Richards A note on sums of independent random variables by P. Hitczenko and S. Montgomery-Smith Exponential integrability of diffusion processes by Y. Hu Local dependencies in random fields via a Bonferroni-type inequality by A. Jakubowski and J. Rosinski Pricing-differentials and bounds for lookback options, and prophet problems in probability by R. P. Kertz A correlation inequality for stable random vectors by A. Koldobsky A note on the maximal inequalities for VC classes by R. Latala Comparison of moments via Poincare-type inequality by K. Oleszkiewicz Fractional sums and integrals of $r$-concave tails and applications to comparison probability inequalities by I. Pinelis Product formula, tails and independence of multiple stable integrals by J. Rosinski and G. Samorodnitsky A domination inequality for martingale polynomials by J. Szulga A log-concavity proof for a Gaussian exponential bound by R. A. Vitale.
£103.50
MP-AMM American Mathematical Stochastic Integrals
Book SynopsisPresents Brownian motion and deals with stochastic integrals and differentials, including Ito lemma. This book is devoted to topics of stochastic integral equations and stochastic integral equations on smooth manifolds. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.Table of ContentsBrownian motion Stochastic integrals and differentials Stochastic integral equations $(d=1)$ Stochastic integral equations $(d\geq2)$ References Subject index Errata.
£54.90
MP-AMM American Mathematical An Introduction to Stochastic Differential
Book SynopsisProvides a quick, but very readable introduction to stochastic differential equations—that is, to differential equations subject to additive “white noise" and related random disturbances. The exposition is strongly focused upon the interplay between probabilistic intuition and mathematical rigour.Trade Review... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too." - MAA ReviewsTable of Contents Preface Introduction A crash course in probability theory Brownian motion and “white noise” Stochastical integrals Stochastic differential equations Applications Appendix Exercises Notes and suggested reading Bibliography Index
£35.96
Springer Nature Switzerland AG Stochastic Processes in Cell Biology: Volume II
Book SynopsisThis book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes – Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.Table of ContentsSensing the environment.- Intracellular pattern formation and reaction-diffusion processes.- Statistical mechanics and dynamics of polymers and membranes.- Self-organization and assembly of cellular structures.- Dynamics and regulation of the cytoskeleton.- Bacterial population growth and collective behavior.- Stochastic reaction-diffusion processes.
£999.99
Springer International Publishing AG Stationary Processes and Discrete Parameter
Book SynopsisThis textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff’s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth–death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.Table of ContentsSymbol Definition List.- 1. Fourier Analysis: A Brief.- 2. Weakly Stationary Processes and their Spectral Measures.- 3. Spectral Representation of Stationary Processes.- 4. Birkhoff’s Ergodic Theorem.- 5. Subadditive Ergodic Theory.- 6. An Introduction to Dynamical Systems.- 7. Markov Chains.- 8. Markov Processes with General State Space.- 9. Stopping Times and the Strong Markov Property.- 10. Transience and Recurrence of Markov Chains.- 11. Birth–Death Chains.- 12. Hitting Probabilities & Absorption.- 13. Law of Large Numbers and Invariant Probability for Markov Chains by Renewal Decomposition.- 14. The Central Limit Theorem for Markov Chains by Renewal Decomposition.- 15. Martingale Central Limit Theorem.- 16. Stationary Ergodic Markov Processes: SLLN & FCLT.- 17. Linear Markov Processes.- 18. Markov Processes Generated by Iterations of I.I.D. Maps.- 19. A Splitting Condition and Geometric Rates of Convergence to Equilibrium.- 20. Irreducibility and Harris Recurrent Markov Processes.- 21. An Extended Perron–Frobenius Theorem and Large Deviation Theory for Markov Processes.- 22. Special Topic: Applications of Large Deviation Theory.- 23. Special Topic: Associated Random Fields, Positive Dependence, FKG Inequalities.- 24. Special Topic: More on Coupling Methods and Applications.- 25. Special Topic: An Introduction to Kalman Filter.- A. Spectral Theorem for Compact Self-Adjoint Operators and Mercer’s Theorem.- B. Spectral Theorem for Bounded Self-Adjoint Operators.- C. Borel Equivalence for Polish Spaces.- D. Hahn–Banach, Separation, and Representation Theorems in Functional Analysis.- References.- Author Index.- Subject Index.
£40.49
Springer International Publishing AG Local Limit Theorems for Inhomogeneous Markov
Book SynopsisThis book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains.The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.Table of Contents- 1. Overview. - 2. Markov Arrays, Additive Functionals, and Uniform Ellipticity. - 3. Variance Growth, Center-Tightness, and the Central Limit Theorem. - 4. The Essential Range and Irreducibility. - 5. The Local Limit Theorem in the Irreducible Case. - 6. The Local Limit Theorem in the Reducible Case. - 7. Local Limit Theorems for Moderate Deviations and Large Deviations. - 8. Important Examples and Special Cases. - 9. Local Limit Theorems for Markov Chains in Random Environments.
£999.99
Springer International Publishing AG Random Measures, Theory and Applications
Book SynopsisOffering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.Trade Review“The theory of random measures is an important point of view of modern probability theory. This is an encyclopedic monograph and the first book to give a systematic treatment of the theory. … the general theory presented in this book is therefore of great importance, far beyond the applications presented here. The book is bound to become the standard reference on the subject.” (Frank Aurzada, Mathematical Reviews, June, 2018)“This book deals with a different aspects of the theory of random measures. … this is a useful book for a researcher in probability theory and mathematical statistics. It is very carefully written and collects results which are not easy to find in the literature or even forgotten.” (Nikolai N. Leonenko, zbMATH 1376.60003, 2018)Table of ContentsPreface.- 1.Spaces, Kernels, and Distribution.- 2.Dissection Limits and Regularity.- 3.Poisson and Related Processes.- 4.Convergence and Approximation.- 5.Stationarity in Euclidean Spaces.- 6.Palm and Related Kernels.- 7.Group Stationarity and Invariance.- 8.Exterior Conditioning.- 9.Compensation and Time Change.- 10.Multiple Integration and Chaos.- 11.Line and Flat Processes.- 12.Regeneration and Local Time.- 13.Branching and Superprocesses.- Appendices.- Historical and Bibliographical Notes.- References.- Indices.
£123.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Probability in Banach Spaces: Isoperimetry and
Book SynopsisIsoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.Trade ReviewThis book gives an excellent, almost complete account of the whole subject of probability in Banach spaces, a branch of probability theory that has undergone vigorous development... There is no doubt in the reviewer's mind that this book [has] become a classic. MathSciNetAs the authors state, "this book tries to present some of the main aspects of the theory of probability in Banach spaces, from the foundation of the topic to the latest developments and current research questions''. The authors have succeeded admirably… This very comprehensive book develops a wide variety of the methods existing … in probability in Banach spaces. … It [has] become an event for mathematicians… Zentralblatt MATHTable of ContentsNotation.- 0. Isoperimetric Background and Generalities.- 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon.- 2. Generalities on Banach Space Valued Random Variables and Random Processes.- I. Banach Space Valued Random Variables and Their Strong Limiting Properties.- 3. Gaussian Random Variables.- 4. Rademacher Averages.- 5. Stable Random Variables.- 6 Sums of Independent Random Variables.- 7. The Strong Law of Large Numbers.- 8. The Law of the Iterated Logarithm.- II. Tightness of Vector Valued Random Variables and Regularity of Random Processes.- 9. Type and Cotype of Banach Spaces.- 10. The Central Limit Theorem.- 11. Regularity of Random Processes.- 12. Regularity of Gaussian and Stable Processes.- 13. Stationary Processes and Random Fourier Series.- 14. Empirical Process Methods in Probability in Banach Spaces.- 15. Applications to Banach Space Theory.- References.
£999.99
World Scientific Publishing Co Pte Ltd Stochastic Komatu-loewner Evolutions
Book SynopsisThe present monograph on stochastic Komatu-Loewner evolutions (SKLEs) provides the first systematic extension of the Schramm-Loewner evolution (SLE) theory from a simply connected planar domain to multiply connected domains by using the Brownian motion with darning (BMD) that has arisen in a recent study of the boundary theory of symmetric Markov processes.This volume is presented in an accessible manner for the interested researchers and graduate students. It also brings new insights into SLEs as special cases of SKLEs. Mathematically, it can be viewed as a powerful application of stochastic analysis via BMDs to complex analysis.
£85.50
Springer Verlag, Singapore Applied Linear Algebra, Probability and
Book SynopsisThis book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.Table of ContentsChapter 1. On Some Matrix Versions of Covariance, Harmonic Mean and other Inequalities: An Overview.- Chapter 2. The Impact of Professor C. R. Rao's Research used in solving problems in Applied Probability.- Chapter 3. Upper ounds for the Euclidean distances between the BLUEs under the partitioned linear fixed model and the corresponding mixed model.- Chapter 4. Nucleolus Computation for some Structured TU Games via Graph Theory and Linear Algebra.- Chapter 5. From Linear System of Equations to Artificial Intelligence - The evolution Journey of Computer Tomographic Image Reconstruction Algorithms.- Chapter 6. Shapley Value and other Axiomatic Extensions to Shapley Value.- Chapter 7. An Accelerated Block Randomized Kaczmarz Methos.- Chapter 8. Nullity of Graphs - A Survey and Some New Results.- Chapter 9. Some Observations on Algebraic Connectivity of Graphs.- Chapter 10. Orthogonality for iadjoints f Operators.- Chapter 11. Permissible covariance structures for simultaneous retention of BLUEs in small and big linear models.- Chapter 12. On some Special Matrices and its Applications in Linear Complementarity Problem.- Chapter 3. On Nearest Matrix with Partially Specified Eigen Structure.- Chapter 14. Equality of BLUEs for Full, Small, and Intermediate Linear Models under Covariance Change, with links to Data Confidentiality and Encryption.-Chapter 15. Statistical Inference for Middle Censored Data with Applications. etc
£999.99
