This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to PDEs, an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of It 's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition reinstates discussion about the central limit theorem for martingales and stationary sequences.

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Bibliographic Details

Title: Probability: Theory and Examples
Publisher: Cengage Learning, Inc
Publication Date: 1995
Language: English
ISBN 10: 0534243185
ISBN 13: 9780534243180
Binding: Hardback
Edition: 2nd Edition
Condition: Very Good

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Synopsis

Modern and measure-theory based, this text is intended primarily for the first-year graduate course in probability theory.

About the Author

Ph.D. Stanford University

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