Probability: Theory and Examples

by Richard Durrett

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 partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of Itô'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 re-instates discussion about the central limit theorem for martingales and stationary sequences.

Genres: Mathematics, Textbooks, Science

431 pages, Kindle Edition

First published January 1, 1990

About the author

Richard Timothy Durrett is a mathematician known for his research and books on mathematical probability theory, stochastic processes and their application to mathematical ecology and population genetics.

He received his BS and MS at Emory University in 1972 and 1973 and his Ph.D. at Stanford University in 1976 under advisor Donald Iglehart. From 1985 until 2010 was on the faculty at Cornell University. Since 2010, Durrett has been a professor at Duke University.

He was elected to the United States National Academy of Sciences in 2007. In 2012 he became a fellow of the American Mathematical Society.[1]

Durrett is the founder of the Cornell Probability Summer Schools, and he is still its scientific organizer.

Reviews

[Anthony Hu · Rating 4 out of 5]

kicking my ass in grad school

[Daniel · Rating 5 out of 5]

Clear and comprehensive; with end-of-chapter exercises.