Stochastics Books

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Book SynopsisPreface * 1. Preliminaries: Discrete Index Sets and/or Discrete State Spaces * 2. Markov Chains * 3. Renewal Theory * 4. Point Processes * 5. Continuous Time Markov Chains * 6. Brownian Motion * 7. The General Random Walk * References * IndexTrade Review"Definitely the best textbook for a second course in probability now available. Written with excruciating lucidity, and with an excellent choice of exercises." —Gian-Carlo Rota, The Bulletin of Mathematics Books "In summary, Resnick has succeeded [in writing] a very fine textbook which will become popular among students as well as among professors preparing an introductory course on stochastic processes." —Internationale Mathematische Nachrichten "A splendid book to bring home the value and importance of stochastic processes. Highly recommended." —Choice "There are so many good introductory texts on [stochastic processes] that one can hardly hope to write a better or more attractive one. This book, however, convinced the reviewer that it very likely that the Adventures will beocme a widely used, popular first year graduate text on stochastic processes. The book is flexible, the motivations of deep theories are clear, the examples and exercises are interesting." ---Zentralblatt MATHTable of ContentsPreface * 1. Preliminaries: Discrete Index Sets and/or Discrete State Spaces * 2. Markov Chains * 3. Renewal Theory * 4. Point Processes * 5. Continuous Time Markov Chains * 6. Brownian Motion * 7. The General Random Walk * References * Index

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Book Synopsis1 Measure Theory.- 2 Integration.- 3 Fourier Analysis.- Appendix A Metric Spaces.- Appendix C A Non-Measurable Subset of the Interval (0, 1].- References.Trade Review"…the text is user friendly to the topics it considers and should be very accessible…Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical AssociationTable of Contents1 Measure Theory.- 2 Integration.- 3 Fourier Analysis.- Appendix A Metric Spaces.- Appendix C A Non-Measurable Subset of the Interval (0, 1].- References.

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Book SynopsisInstead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance and engineering.Trade ReviewFrom the reviews:“This introduction to measure-theoretic probability is intended for students whose primary interest is not mathematics but statistics, engineering, biology, or finance. The book is a welcome reprint in paperback … . The book’s pace … is ‘quick and disciplined’.” (William J. Satzer, MAA Reviews, March, 2014)Table of Contents1 Sets and Events.- 2 Probability Spaces.- 3 Random Variables, Elements and Measurable Maps.- 4 Independence.- 5 Integration and Expectation.- 6 Convergence Concepts.- 7 Laws of Large Numbers and Sums of Independent Random Variables.- 8 Convergence in Distribution.- 9 Characteristic Functions and the Central Limit Theorem.- 10 Martingales.- Index.- References.

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Book SynopsisThis textbook presents the design and analysis of experiments that comprise the aspects of classical theory for continuous response, modern procedures for categorical response, and especially for correlated categorical response.Trade ReviewFrom the reviews of the second edition:"[This book] is a useful reference or graduate text to complement more common choices for introductory design of experiment books … the methods are logically and thoroughly developed in a rigorous, yet understandable manner. The emphasis on pharmaceutical applications throughout the book is helpful, because this continues to emerge as an important area of applications. The book would be helpful for statisticians and researchers in pharmaceutical areas once they had gained a solid understanding of the fundamentals of design of experiments." –Journal of the American Statistical Association"The second edition of this book … has been reorganized with a list of topics similar to that of the first edition, but with a revised presentation and order. … much greater emphasis now placed on the analysis aspect of design of experiments. … a useful reference book or graduate text … . The methods are logically and thoroughly developed in a rigorous, yet understandable manner. … The book would be helpful for statisticians and researchers in pharmaceutical areas … ." (Christine M. Anderson Cook, Journal of the American Statistical Association, Vol. 98 (463), 2003)"This book is mostly concerned with the mathematical detail of the topics in the contents. There are a few sets of data, to illustrate the material; on these, SAS, S-PLUS or SPSS is used for analysis. … This would be an excellent book for mathematics students who take a course in statistics, or graduate statistic students … ." (N. R. Draper, Short Book Reviews, Vol. 23 (1), 2003)"Helge Toutenburg describes this text as a ‘resource/reference book which contains statistical methods used by researchers in applied areas.’ … the theory is described in a shorthand style that gets to the point without overburdening the reader with mathematical detail … . the author includes thorough discussions of generalized linear models (categorical data analysis) and repeated-measures designs. … a useful, self-contained reference for those who want a quick description of the underlying theory and practice for a large assortment of standard DOE problems." (Peter Wludyka, Technometrics, Vol. 45 (2), May, 2003)From the reviews of the third edition:“This book provides matter related to experimental designs which are of practical relevance. One can understand the subject matter without knowledge of high level mathematics. The book is suitable as a textbook for courses on experimental design in universities and institutions and as a resource book for researchers.” (B. L. Agarwal, Zentralblatt MATH, Vol. 1211, 2011)Table of ContentsComparison of Two Samples.- The Linear Regression Model.- Single#x2013;Factor Experiments with Fixed and Random Effects.- More Restrictive Designs.- Incomplete Block Designs.- Multifactor Experiments.- Models for Categorical Response Variables.- Repeated Measures Model.- Cross#x2013;Over Design.- Statistical Analysis of Incomplete Data.

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Book SynopsisBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.Trade ReviewFrom the reviews:“Robert and Casella’s new book uses the programming language R, a favorite amongst (Bayesian) statisticians to introduce in eight chapters both basic and advanced Monte Carlo techniques … . The book could be used as the basic textbook for a semester long course on computational statistics with emphasis on Monte Carlo tools … . useful for (and should be next to the computer of) a large body of hands on graduate students, researchers, instructors and practitioners … .” (Hedibert Freitas Lopes, Journal of the American Statistical Association, Vol. 106 (493), March, 2011)“Chapters focuses on MCMC methods the Metropolis–Hastings algorithm, Gibbs sampling, and monitoring and adaptation for MCMC algorithms. … There are exercises within and at the end of all chapters … . Overall, the level of the book makes it suitable for graduate students and researchers. Others who wish to implement Monte Carlo methods, particularly MCMC methods for Bayesian analysis will also find it useful.” (David Scott, International Statistical Review, Vol. 78 (3), 2010)“The primary audience is graduate students in statistics, biostatistics, engineering, etc. who need to know how to utilize Monte Carlo simulation methods to analyze their experiments and/or datasets. … this text does an effective job of including a selection of Monte Carlo methods and their application to a broad array of simulation problems. … Anyone who is an avid R user and has need to integrate and/or optimize complex functions will find this text to be a necessary addition to his or her personal library.” (Dean V. Neubauer, Technometrics, Vol. 53 (2), May, 2011)Table of ContentsBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.

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Book SynopsisAt the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.Trade ReviewFrom the reviews: "This is certainly a very valuable book for anyone interested in this new methodology." N.D.C. Veraverbeke for Short Book Reviews of the ISI, December 2006 "The present book does bring something new and, indeed some novel theoretical investigations into the kinds of functional data problems … . I do think the present book is a worthy contribution to the literature. The authors have done a nice job of summarizing some of ongoing research … . Researchers in the growing functional statistics community should be glad to have a copy of the book." (Z. Q. John Lu, Technometrics, Vol. 49 (2), 2007) "This book presents new nonparametric staustical methods for samples of functional data … . The computational aspects of the book are oriented toward practitioners whereas open problems emerging from this new field of statistics will attract Ph. D. students and academic researchers. This book is also accessible to graduate students starting out in the area of functional statistics." (Fazil A. Aliev, Mathematical Reviews, Issue 2007 b) "Nonparametric Functional Data Analysis explores nonparametric methods as that can be applied to functional data, developing new methods and providing theoretical results for the conditional and unconditional mean, median, and mode for independent and dependent functional data. … As a resource for those interested in FDA research and methods, it is highly recommended. … This book should spur new and exciting research in FDA, and it provides new tools that are ready for application to real data sets." (Mark Greenwood, Journal of the American Statistical Association, Vol. 102 (479), 2007) "Example data sets that motivate the development of the models are also provided. … The index provided seems to be fairly complete and is helpful in looking up topics discusses in this monograph. Several chapters end in a section in which the authors provide additional comments, discussions and pose some open problems in this area, which should be appealing for researchers in this field. … This book should be useful for all people interested in the area of functional data analysis." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1119 (21), 2007)Table of ContentsIntroduction to functional nonparametric statistics.- Some functional datasets and associated statistical problematics.- What is a well adapted space for functional data?.- Local weighting of functional variables.- Functional nonparametric prediction methodologies.- Some selected asymptotics.- Computational issues.- Nonparametric supervised classification for functional data.- Nonparametric unsupervised classification for functional data.- Mixing, nonparametric and functional statistics.- Some selected asymptotics.- Application to continuous time processes prediction.- Small ball probabilities, semi-metric spaces and nonparametric statistics.- Conclusion and perspectives.

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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 Basic Concepts and Elementary Models.- 1. The Vocabulary of Probability Theory.- 2. Events and Probability.- 3. Random Variables and Their Distributions.- 4. Conditional Probability and Independence.- 5. Solving Elementary Problems.- 6. Counting and Probability.- 7. Concrete Probability Spaces.- Illustration 1. A Simple Model in Genetics: Mendel's Law and HardyWeinberg's Theorem.- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle.- Illustration 3. Bertrand's Paradox.- 2 Discrete Probability.- 1. Discrete Random Elements.- 2. Variance and Chebyshev's Inequality.- 3. Generating Functions.- Illustration 4. An Introduction to Population Theory: GaltonWatson's Branching Process.- Illustration 5. Shannon's Source Coding Theorem: An Introduction to Information Theory.- 3 Probability Densities.- I. Expectation of Random Variables with a Density.- 2. Expectation of Functionals of Random Vectors.- 3. Independence.- 4. Random Variables That Are Not Discrete anTable of Contents1 Basic Concepts and Elementary Models.- 1. The Vocabulary of Probability Theory.- 2. Events and Probability.- 2.1. Probability Space.- 2.2. Two Elementary Probabilistic Models.- 3. Random Variables and Their Distributions.- 3.1. Random Variables.- 3.2. Cumulative Distribution Function.- 4. Conditional Probability and Independence.- 4.1. Independence of Events.- 4.2. Independence of Random Variables.- 5. Solving Elementary Problems.- 5.1. More Formulas.- 5.2. A Small Bestiary of Exercises.- 6. Counting and Probability.- 7. Concrete Probability Spaces.- Illustration 1. A Simple Model in Genetics: Mendel’s Law and Hardy—Weinberg’s Theorem.- Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle.- Illustration 3. Bertrand’s Paradox.- 2 Discrete Probability.- 1. Discrete Random Elements.- 1.1. Discrete Probability Distributions.- 1.2. Expectation.- 1.3. Independence.- 2. Variance and Chebyshev’s Inequality.- 2.1. Mean and Variance.- 2.2. Chebyshev’s Inequality.- 3. Generating Functions.- 3.1. Definition and Basic Properties.- 3.2. Independence and Product of Generating Functions.- Illustration 4. An Introduction to Population Theory: Galton—Watson’s Branching Process.- Illustration 5. Shannon’s Source Coding Theorem: An Introduction to Information Theory.- 3 Probability Densities.- I. Expectation of Random Variables with a Density.- 1.1. Univariate Probability Densities.- 1.2. Mean and Variance.- 1.3. Chebyshev’s Inequality.- 1.4. Characteristic Function of a Random Variable.- 2. Expectation of Functionals of Random Vectors.- 2.1. Multivariate Probability Densities.- 2.2. Covariance, Cross-Covariance, and Correlation.- 2.3. Characteristic Function of a Random Vector.- 3. Independence.- 3.1. Independent Random Variables.- 3.2. Independent Random Vectors.- 4. Random Variables That Are Not Discrete and Do Not Have a pd.- 4.1. The Abstract Definition of Expectation.- 4.2. Lebesgue’s Theorems and Applications.- Illustration 6. Buffon’s Needle: A Problem in Random Geometry.- 4 Gauss and Poisson.- 1. Smooth Change of Variables.- 1.1. The Method of the Dummy Function.- 1.2. Examples.- 2. Gaussian Vectors.- 2.1. Characteristic Function of Gaussian Vectors.- 2.2. Probability Density of a Nondegenerate Gaussian Vector.- 2.3. Moments of a Centered Gaussian Vector.- 2.4. Random Variables Related to Gaussian Vectors.- 3. Poisson Processes.- 3.1. Homogeneous Poisson Processes Over the Positive Half Line.- 3.2. Nonhomogeneous Poisson Processes Over the Positive Half Line.- 3.3. Homogeneous Poisson Processes on the Plane.- 4. Gaussian Stochastic Processes.- 4.1. Stochastic Processes and Their Law.- 4.2. Gaussian Stochastic Processes.- Illustration 7. An Introduction to Bayesian Decision Theory: Tests of Gaussian Hypotheses.- 5 Convergences.- 1. Almost-Sure Convergence.- 1.1. The Borel—Cantelli Lemma.- 1.2. A Criterion for Almost-Sure Convergence.- 1.3. The Strong Law of Large Numbers.- 2. Convergence in Law.- 2.1. Criterion of the Characteristic Function.- 2.2. The Central Limit Theorem.- 3. The Hierarchy of Convergences.- 3.1. Almost-Sure Convergence Versus Convergence in Probability.- 3.2. Convergence in the Quadratic Mean.- 3.3. Convergence in Law in the Hierarchy of Convergences.- 3.4. The Hierarchical Tableau.- Illustration 8. A Statistical Procedure: The Chi-Square Test.- Illustration 9. Introduction to Signal Theory: Filtering.- Additional Exercises.- Solutions to Additional Exercises.

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Book Synopsis[1] The Taming of Chance.- From Unpredictable to Lawful.- Probability.- Order in the Large.- The Normal Law.- Is It Random?.- More About the Law of Large Numbers.- Where We Stand Now.- [2] Uncertainty and Information.- Messages and Information.- Entropy.- Messages, Codes, and Entropy.- Approximate Entropy.- Again, Is It Random?.- The Perception of Randomness.- [3] Janus-Faced Randomness.- Is Determinism an Illusion?.- Generating Randomness.- Janus and the Demons.- [4] Algorithms, Information, and Chance.- Algorithmic Randomness.- Algorithmic Complexity and Undecidability.- Algorithmic Probability.- [5] The Edge of Randomness.- Between Order and Disorder.- Self-Similarity and Complexity.- What Good is Randomness?.- Sources and Further Readings.- Technical Notes.- Appendix A: Geometric Sums.- Appendix B: Binary Numbers.- Appendix C: Logarithims.- References.Trade ReviewFrom the reviews: THE AMERICAN STATISTICIAN "In summary, I think that many readers with a strong interest in mathematics, statistics, physics, or other areas of science will find this book interesting and challenging. I strongly recommend it to all who are interested in science and would like to see how the ideas of both theoretical mathematics and statistics have been observed and used in real life throughout history." MATHEMATICAL REVIEWS "The book is nicely written and should entertain many readers…"Table of Contents[1] The Taming of Chance.- From Unpredictable to Lawful.- Probability.- Order in the Large.- The Normal Law.- Is It Random?.- More About the Law of Large Numbers.- Where We Stand Now.- [2] Uncertainty and Information.- Messages and Information.- Entropy.- Messages, Codes, and Entropy.- Approximate Entropy.- Again, Is It Random?.- The Perception of Randomness.- [3] Janus-Faced Randomness.- Is Determinism an Illusion?.- Generating Randomness.- Janus and the Demons.- [4] Algorithms, Information, and Chance.- Algorithmic Randomness.- Algorithmic Complexity and Undecidability.- Algorithmic Probability.- [5] The Edge of Randomness.- Between Order and Disorder.- Self-Similarity and Complexity.- What Good is Randomness?.- Sources and Further Readings.- Technical Notes.- Appendix A: Geometric Sums.- Appendix B: Binary Numbers.- Appendix C: Logarithims.- References.

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Book SynopsisThis study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950.Trade ReviewFrom the book reviews:“Fischer provides thorough mathematical descriptions of the development of the central limit theorem as it evolves with increasing mathematical rigor. … Fischer has probably written what will be the definitive history of the central limit theorem for many years to come. … Fischer overflows with detail, insight and excellent commentary.” (David Bellhouse, Historia Mathematica, Vol. 39, 2012)“The book will be of interest not only to professionals in the area of probability and statistics but to a wider audience. … The author has been using a huge amount of sources and archives, including his own works, and he is successful in his goal to describe a comprehensive picture of the development of the CLT. … the book would be an excellent source for student projects on topics from probability and its applications.” (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1226, 2012)“This work details the history of the central limit theorem and related probabilistic limit theorems roughly from 1810 through 1950, but focuses on 1810 to 1935. … Hans Fischer … authors many papers on the history of mathematics. His skill in both these areas allows him to reveal here the historical development of this important theorem in a way that can easy be adapted to the lecture hall or used in independent study.” (Tom Schulte, The Mathematical Association of America, February, 2011)“The history of the CLT deserves a place of its own, and this book by Hans Fischer is the best … in tracing its development in meticulous historical detail and with mathematical precision. … The book by Hans Fischer is highly recommended as a well-researched comprehensive history of the CLT. One finds here the story of a galaxy of brilliant mathematicians … engaging in the quest for, and debates on, the true meaning and the correct derivation of a beautiful intriguing result.”­­­ (Rabi Bhattacharya, SIAM Review, Vol. 53 (4), 2011)Table of ContentsPreface.- Introduction.- The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods.- The hypothesis of elementary errors.- Chebyshev's and markov's contributions.- The way towards modern probability.- General limit problems.- Conclusion: the central limit theorem as a link between classical and modern probability.- Index.- Bibliography

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Book SynopsisThe techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.Trade ReviewFrom the book reviews:“The monograph concentrates on intelligent systems for decision support based on probabilistic models, including Bayesian networks and influence diagrams. … This monograph provides a review of recent state affairs of probabilistic networks that can be useful for professionals, practitioners, and researchers from diverse fields of statistics and related disciplines. I think it can be used as a textbook in its own right for an upper level undergraduate course, especially for a reading course.” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsIntroduction.- Networks.- Probabilities.- Probabilistic Networks.- Solving Probabilistic Networks.- Eliciting the Model.- Modeling Techniques.- Data-Driven Modeling.- Conflict Analysis.- Sensitivity Analysis.- Value of Information Analysis.- Quick Reference to Model Construction.- List of Examples.- List of Figures.- List of Tables.- List of Symbols.- References.- Index.

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Book SynopsisThis book provides a comprehensive up-to-date presentation of some of the classical areas of reliability, based on a more advanced probabilistic framework using the modern theory of stochastic processes.Trade Review This is an excellent book on mathematical, statistical and stochastic models in reliability. The authors have done an excellent job of unifying some of the stochastic models in reliability. The book is a good reference book but may not be suitable as a textbook for students in professional fields such as engineering. This book may be used for graduate level seminar courses for students who have had at least the first course in stochastic processes and some knowledge of reliability mathematics. It should be a good reference book for researchers in reliability mathematics.--Mathematical ReviewsTable of ContentsIntroduction.- Basic Reliability Theory.- Stochastic Failure Models.- Availability Analysis of Complex Systems.- Maintenance Optimization.

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Book SynopsisThis text is concerned with Bayesian learning, inference and forecasting in dynamic environments.Table of Contentsto the DLM: The First-Order Polynomial Model.- to the DLM: The Dynamic Regression Model.- The Dynamic Linear Model.- Univariate Time Series DLM Theory.- Model Specification and Design.- Polynomial Trend Models.- Seasonal Models.- Regression, Autoregression, and Related Models.- Illustrations and Extensions of Standard DLMs.- Intervention and Monitoring.- Multi-Process Models.- Non-Linear Dynamic Models: Analytic and Numerical Approximations.- Exponential Family Dynamic Models.- Simulation-Based Methods in Dynamic Models.- Multivariate Modelling and Forecasting.- Distribution Theory and Linear Algebra.

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Book SynopsisThis book covers the basic results and methods in probability theory. This new edition offers updated content, 100 additional problems for solution, and a new chapter glimpsing further topics such as stable distributions, domains of attraction and martingales.Trade ReviewFrom the reviews of the second edition:"This is an excellent introductory book on random variables, with a wealth of examples and exercises. … The material is very well organized … . The text is remarkably well written, mathematically and aesthetically; layout and fonts make it a pleasant reading, and the examples are often enlightening. I think it will be a valuable support for students and instructors and it should definitely find a place in every good library." (Fabio Mainardi, The Mathematical Association of America, October, 2009)“…A worthwhile addition to the textbook pool, one that will guide the student safely through to a point of competence and ability to embark on a more advanced study…” (International Statistical Review, 2010, 78, 1, 134-159)“The book addresses a unique niche mathematically inclined students previously exposed to an introductory course in probability … . The writing style is lucid and easy to follow. … book is clearly directed toward mathematicians and the highly mathematically inclined scientist or engineer who might be induced to study the mathematics of probability or mathematical statistics. For those who find the classical mathematical pedagogy motivating or those requiring a comprehensive readable reference work on the mathematics of probability theory the book can be highly recommended.” (Thomas D. Sandry, Technometrics, Vol. 53 (1), February, 2011)“This book … is intended as an introductory graduate level textbook in probability for statistics majors. … This book provides an elaborate description and a collection of results in probability theory. … The level of this book is suitable for a graduate course. Overall all concepts are well discussed with full mathematical rigor. … has a good collection of most of the results related to probability theory, the price is very reasonable, and I will recommend this book to university mathematics and statistics libraries.” (Sounak Chakraborty, Journal of the American Statistical Association, Vol. 106 (495), September, 2011)Table of ContentsMultivariate Random Variables.- Conditioning.- Transforms.- Order Statistics.- The Multivariate Normal Distribution.- Convergence.- An Outlook on Further Topics.- The Poisson Process.

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Book SynopsisIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups.Trade ReviewFrom the book reviews:“This textbook provides a comprehensive and consistent introduction to measure and integration theory. … The book can be recommended to anyone having basic knowledge of calculus and point-set topology. It is very self-contained, and can thus serve as an excellent reference book as well.” (Ville Suomala, Mathematical Reviews, July, 2014)“In this second edition, Cohn has updated his excellent introduction to measure theory … and has made this great textbook even better. Those readers unfamiliar with Cohn’s style will discover that his writing is lucid. … this is a wonderful text to learn measure theory from and I strongly recommend it.” (Tushar Das, MAA Reviews, June, 2014)Table of Contents1. Measures.- Algebras and sigma-algebras.- Measures.- Outer measures.- Lebesgue measure.- Completeness and regularity.- Dynkin classes.- 2. Functions and Integrals.- Measurable functions.- Properties that hold almost everywhere.- The integral.- Limit theorems.- The Riemann integral.- Measurable functions again, complex-valued functions, and image measures.- 3. Convergence.- Modes of Convergence.- Normed spaces.- Definition of L^p and L^p.- Properties of L^p and L-p.- Dual spaces.- 4. Signed and Complex Measures.- Signed and complex measures.- Absolute continuity.- Singularity.- Functions of bounded variation.- The duals of the L^p spaces.- 5. Product Measures.- Constructions.- Fubini’s theorem.- Applications.- 6. Differentiation.- Change of variable in R^d.- Differentiation of measures.- Differentiation of functions.- 7. Measures on Locally Compact Spaces.- Locally compact spaces.- The Riesz representation theorem.- Signed and complex measures; duality.- Additional properties of regular measures.- The µ^*-measurable sets and the dual of L^1.- Products of locally compact spaces.- 8. Polish Spaces and Analytic Sets.- Polish spaces.- Analytic sets.- The separation theorem and its consequences.- The measurability of analytic sets.- Cross sections.- Standard, analytic, Lusin, and Souslin spaces.- 9. Haar Measure.- Topological groups.- The existence and uniqueness of Haar measure.- The algebras L^1 (G) and M (G).- Appendices.- A. Notation and set theory.- B. Algebra.- C. Calculus and topology in R^d.- D. Topological spaces and metric spaces.- E. The Bochner integral.- F Liftings.- G The Banach-Tarski paradox.- H The Henstock-Kurzweil and McShane integralsBibliography.- Index of notation.- Index.

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Book SynopsisThe techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.Trade ReviewFrom the book reviews:“The monograph concentrates on intelligent systems for decision support based on probabilistic models, including Bayesian networks and influence diagrams. … This monograph provides a review of recent state affairs of probabilistic networks that can be useful for professionals, practitioners, and researchers from diverse fields of statistics and related disciplines. I think it can be used as a textbook in its own right for an upper level undergraduate course, especially for a reading course.” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsIntroduction.- Networks.- Probabilities.- Probabilistic Networks.- Solving Probabilistic Networks.- Eliciting the Model.- Modeling Techniques.- Data-Driven Modeling.- Conflict Analysis.- Sensitivity Analysis.- Value of Information Analysis.- Quick Reference to Model Construction.- List of Examples.- List of Figures.- List of Tables.- List of Symbols.- References.- Index.

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Trade Review“This book is the result … of a fruitful and long collaboration between a mathematician and a cell biologist. Capturing the best of both worlds, the book provides not only the biology and mathematical background for this topic, but also offers numerous examples which render it accessible to (post-graduate) students and researchers … . this book can be treated as an excellent textbook for a wide audience varying from students to lecturers.” (Irina Ioana Mohorianu, zbMATH 1312.92004, 2015)"This book treats the theory of several important types of branching processes and demonstrates their usefulness by many interesting and important applications. … Mathematical theory and biological applications are nicely interwoven. This text will be useful both to mathematicians (including graduate students) interested in relevant applications of stochastic processes in biology, as well as to mathematically oriented biologists working on the above mentioned topics." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (1), 2004)"This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Charles J. Mode, Siam Review, Vol. 45 (2), 2003)"This is a book written jointly by a mathematician and a cell biologist, who have collaborated on research in branching processes for more than a decade. In their own words, their monograph is intended for ‘mathematicians and statisticians who have had an introduction to stochastic processes but have forgotten much of their college biology, and for biologists who wish to collaborate with mathematicians and statisticians.’ They have largely succeeded in achieving their goal. The book can be strongly recommended to all students of branching processes; all libraries should have a copy." —ZENTRALBLATT MATH Table of ContentsMotivating Examples and Other Preliminaries.- Biological Background.- The Galton-Watson Process.- The Age-Dependent Process: Markov Case.- The Bellman-Harris Process.- Multitype Processes.- Branching Processes with Infinitely Many Types.- Genealogies of Branching Processes and their Applications.- References.

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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 SynopsisThis two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.Trade Review“The text is very well-written and can be used to study the theory on various levels. It develops systematically from the wealth of motivating examples and heuristical considerations, through the carefully chosen collection of in-depth explained preliminaries, to the extensive nontrivial theory explained in full detail. … The book is highly recommended for those interested in the foundations and the up-to-date development of MFGs, as well as in the general area of stochastic control and related issues of analysis and probability.” (Vassili, Mathematical Reviews, January, 2019)Table of ContentsPreface to Volume I.- Part I: The Probabilistic Approach to Mean Field Games.- Learning by Examples: What is a Mean Field Game?.- Probabilistic Approach to Stochastic Differential Games.- Stochastic Differential Mean Field Games.- FBSDEs and the Solution of MFGs without Common Noise.- Part II: Analysis on Wasserstein Space and Mean Field Control.- Spaces of Measures and Related Differential Calculus.- Optimal Control of SDEs of McKean-Vlasov Type.- Epologue to Volume I.- Extensions for Volume I. References.- Indices.

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Book SynopsisFocussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.Table of Contents- Part I Stochastic Epidemics in a Homogeneous Community. - Introduction. - Stochastic Epidemic Models. - Markov Models. - General Closed Models. - Open Markov Models. - Part II Stochastic SIR Epidemics in Structured Populations. - Introduction. - Single Population Epidemics. - The Households Model. - A General Two-Level Mixing Model. - Part III Stochastic Epidemics in a Heterogeneous Community. - Introduction. - Random Graphs. - The Reproduction Number R0. - SIR Epidemics on Configuration Model Graphs. - Statistical Description of Epidemics Spreading on Networks: The Case of Cuban HIV. - Part IV Statistical Inference for Epidemic Processes in a Homogeneous Community. - Introduction. - Observations and Asymptotic Frameworks. - Inference for Markov Chain Epidemic Models. - Inference Based on the Diffusion Approximation of Epidemic Models. - Inference for Continuous Time SIR models.

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Book SynopsisThis textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk. It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.Table of ContentsBasics.- Experience Rating.- Sums and Aggregate Claims.- Ruin Theory.- Markov Models in Life Insurance.- Financial Mathematics in Life Insurance.- Special Studies in Life Insurance.- Orderings and Comparisons.- Extreme Value Theory.- Dependence and Further Topics in Risk Management.- Stochastic Control in Non-Life Insurance.- Stochastic Control in Life Insurance.- Selected Further Topics.

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