Brownian Motion van Peter Moerters and Yuval Peres is an English-language textbook focused on the theory of Brownian motion. This reference work is intended for the graduate student in probability theory and provides a comprehensive treatment of both fundamental concepts and recent lines of research.
This eagerly awaited book covers everything that the graduate student wants to know about Brownian motion. The book begins with the construction of the process, followed by properties of sample paths such as continuity and nowhere differentiability. Fractal dimensions are introduced and used to describe fine properties of Brownian paths. The relationship between Brownian motion and random walk is also treated extensively, including the theory of local times.
In addition, it includes an accessible explanation of stochastic integration and potential theory, and discusses the intersections of Brownian paths. Finally, the authors treat exceptional points and include an appendix on SLE processes by Oded Schramm and Wendelin Werner, thereby connecting the book to modern research topics.
In terms of content, this title relates to topics such as Materials / States of matter, Probability and statistics, and Physics / General. Series: Cambridge Series in Statistical and Probabilistic Mathematics