ENGLISH

Brownian Motion

By Yuval Peres , Peter Mörters

Book information

Publisher
Cambridge University Press
Year
2010
ISBN
0521760186, 9780521760188
Language
english
Format
PDF
Filesize
4 MB (4514340 bytes)
Series
Cambridge Series in Statistical and Probabilistic Mathematics
Edition
1
Pages
417\417
Time added
2010-06-26 00:49:36

Description

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.

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