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Probability Theory: An Analytic View, by Daniel W. Stroock
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This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given. The first part of the book deals with independent random variables, Central Limit phenomena, and the construction of Levy processes, including Brownian motion. Conditioning is developed and applied to discrete parameter martingales in Chapter 5, Chapter 6 contains the ergodic theorem and Burkholder's inequality, and continuous parameter martingales are discussed in Chapter 7. Chapter 8 is devoted to Gaussian measures on a Banach space, where they are treated from the abstract Wiener space perspective. The abstract theory of weak convergence is developed in Chapter 9, which ends with a proof of Donsker's Invariance Principle. The concluding two chapters contain applications of Brownian motion to the analysis of partial differential equations and potential theory.
- Sales Rank: #1871021 in Books
- Published on: 2010-12-31
- Released on: 2011-03-10
- Original language: English
- Number of items: 1
- Dimensions: 9.96" h x 1.10" w x 8.46" l, 2.02 pounds
- Binding: Paperback
- 548 pages
Review
"The first edition has already taken its place among the classics of probability theory, and this second edition deserves its own place on that shelf."
Ofer Zeitouni, Mathematical Reviews
"What distinguishes this book from the sea of textbooks on probability theory is the stress on analysis and its nontraditional structure. I am really pleased with the examples and exercises at the end of each paragraph, which are a valuable part of the book. This is an excellent, clearly written text that can be used in graduate and independent study."
Alexander Tzanov, Computing Reviews
About the Author
Dr Daniel W. Stroock is the Simons Professor of Mathematics Emeritus at the Massachusetts Institute of Technology. He has published numerous articles and is the author of six books, most recently Partial Differential Equations for Probabilists (2008).
Most helpful customer reviews
11 of 14 people found the following review helpful.
Probability Theory, An Analyitic View, 2nd Edition
By Daniel W. Stroock
In spite of my best efforts to avoid them, this book is riddled with annoying errors. Most of them are minor, but some of them more serious. I am compiling a growing errata list in a pdf file which can be downloaded from
[...]
Obviously, my "rating" of this item should be ignored. I rated it simply to comply with Amazon's rules.
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