Probability Theory
An Analytic View

A second edition of Daniel W. Stroock's classic probability theory textbook suitable for first-year graduate students with a good grasp of introductory, undergraduate probability.

Daniel W. Stroock (Author)

9780521132503, Cambridge University Press

Paperback, published 31 December 2010

548 pages, 768 exercises
25.4 x 17.9 x 2.7 cm, 0.91 kg

'… uniformly well written and well spiced with comments to aid the intuition, so the readership should include a wide range, both of students and of professional probabilists. … We can expect it to take its place alongside the classics of probability theory.' Mathematical Reviews

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.

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.

Subject Areas: Probability & statistics [PBT], Calculus & mathematical analysis [PBK]