A Basic Course in Probability Theory
Authors: Bhattacharya, Rabi, Waymire, Edward C.
Free Preview Quicker paced introduction to the basics allows for a more indepth treatment of such topics as convergence theory and Brownian motion
 Selfcontained and suitable for students with varying levels of background in analysis and measure theory
 Includes a complete overview of basic measure theory as well as analysis, with proofs
 Written in a lively and engaging style
 Contains an extensive bibliography pointing readers to further study
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 About this Textbook

The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wideranging applications. With this goal in mind, the pace is lively, yet thorough. Basic notions of independence and conditional expectation are introduced relatively early on in the text, while conditional expectation is illustrated in detail in the context of martingales, Markov property and strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two highlights. The historic role of sizebiasing is emphasized in the contexts of large deviations and in developments of Tauberian Theory.
The authors assume a graduate level of maturity in mathematics, but otherwise the book will be suitable for students with varying levels of background in analysis and measure theory. In particular, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference.
Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have coauthored numerous books, including the graduate textbook, Stochastic Processes with Applications.
 Reviews

From the reviews:
"Bhattacharya (Univ. of Arizona, Tucson) and Waymire (Oregon State Univ., Corvallis) write to provide the necessary probability background for studying stochastic processes. For students exposed to analysis and measure theory, the book can be used as a graduatelevel course resource on probability. … Every chapter ends with a set of exercises, including numerous solved examples. Appendixes explain measure theory and integration, function spaces and topology, and Hilbert spaces and applications to measure theory. List of symbols. Summing Up: Recommended. Graduate students; faculty and researchers." (D. V. Chopra, CHOICE, Vol. 45 (7), 2008)
"The mentioned prerequisites are exposure to measure theory and analysis. Three appendices (29 pages) provide a brief but thorough introduction to the measure theory and functional analysis that is needed. … This wellwritten book is full of wonderful probability theory." (Kenneth A. Ross, MathDL, February, 2008)
"The book provides the fundamentals of probability theory in a measuretheoretic framework ... . is suitable for advanced undergraduate students and graduate students. The material is presented in a very dense and concise way and each chapter includes a section with exercises at the end ... . Thus the book may be used very well as a reference text and companion literature for a lecture course ... ." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1138 (16), 2008)
"This book is a selfcontained exposition of various basic elements of probability theory. It is suitable for graduate students with some background in analysis, but may also serve as a quick reference for more experienced readers. … Overall, this book is quite rich and very pleasant to read … ." (Djalil Chafaï, Mathematical Reviews, Issue 2009 e)
 Table of contents (13 chapters)


Random Maps, Distribution, and Mathematical Expectation
Pages 117

Independence, Conditional Expectation
Pages 1936

Martingales and Stopping Times
Pages 3748

Classical Zero–One Laws, Laws of Large Numbers and Deviations
Pages 4958

Weak Convergence of Probability Measures
Pages 5972

Table of contents (13 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 A Basic Course in Probability Theory
 Authors

 Rabi Bhattacharya
 Edward C. Waymire
 Series Title
 Universitext
 Copyright
 2007
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9780387719399
 DOI
 10.1007/9780387719399
 Series ISSN
 01725939
 Edition Number
 1
 Number of Pages
 XII, 220
 Topics