Celebrate the holidays with Apress Access for just $/£/€ 99! Universitext # A Basic Course in Probability Theory Authors: Bhattacharya, Rabi, Waymire, Edward C. Free Preview • Quicker paced introduction to the basics allows for a more in-depth treatment of such topics as convergence theory and Brownian motion • Self-contained 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 see more benefits ### Buy this book eBook$44.99
price for USA (gross)
• ISBN 978-0-387-71939-9
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices

The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging 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 size-biasing 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 co-authored 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 graduate-level 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 well-written book is full of wonderful probability theory." (Kenneth A. Ross, MathDL, February, 2008)

"The book provides the fundamentals of probability theory in a measure-theoretic 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 self-contained 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)

• Random Maps, Distribution, and Mathematical Expectation

Pages 1-17

• Independence, Conditional Expectation

Pages 19-36

• Martingales and Stopping Times

Pages 37-48

• Classical Zero–One Laws, Laws of Large Numbers and Deviations

Pages 49-58

• Weak Convergence of Probability Measures

Pages 59-72

eBook \$44.99
price for USA (gross)
• ISBN 978-0-387-71939-9
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices

## Bibliographic Information

Bibliographic Information
Book Title
A Basic Course in Probability Theory
Authors
Series Title
Universitext
2007
Publisher
Springer-Verlag New York