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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.Read more
- Presents a novel selection and treatment of probability theory
- The reader will see how probability theory can be used in other branches of mathematics
Reviews & endorsements
"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 ReviewsSee more 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
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- Edition: 2nd Edition
- Date Published: December 2010
- format: Paperback
- isbn: 9780521132503
- length: 548 pages
- dimensions: 251 x 178 x 30 mm
- weight: 0.92kg
- contains: 768 exercises
- availability: Available
Table of Contents
1. Sums of independent random variables
2. The central limit theorem
3. Infinitely divisible laws
4. Levy processes
5. Conditioning and martingales
6. Some extensions and applications of martingale theory
7. Continuous parameter martingales
8. Gaussian measures on a Banach space
9. Convergence of measures on a Polish space
10. Wiener measure and partial differential equations
11. Some classical potential theory.
Instructors have used or reviewed this title for the following courses
- MATH FOR TEACHERS
- Topics in Mathematical Probability
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