Probability Theory: An Analytic View pdf epub fb2

Probability Theory: An Analytic View by Daniel W. Stroock pdf epub fb2 djvu

Author: Daniel W. Stroock
Title: Probability Theory: An Analytic View
ISBN: 0521761581
ISBN13: 978-0521761581
Other Formats: azw mobi mbr txt
Pages: 550 pages
Publisher: Cambridge University Press; 2 edition (December 31, 2010)
Language: English
Size PDF version: 1902 kb
Size EPUB version: 1277 kb
Category: Science & Math
Subcategory: Mathematics

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.

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