Brownian motion

Peter Morters, Yuval Peres

Research output: Book/ReportBook

Abstract

This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.
Original languageEnglish
Place of PublicationCambridge
PublisherCambridge University Press
Volume30
ISBN (Print)9780521760188
Publication statusPublished - 2010

Publication series

NameCambridge Series in Statistical and Probabilistic Mathematics
PublisherCambridge University Press

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    Morters, P., & Peres, Y. (2010). Brownian motion. (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge University Press.