Brownian motion

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 differe...

Full description

Bibliographic Details
Main Authors: Mörters, Peter, Peres, Y. (Author), Schramm, Oded (Author), Werner, Wendelin (Author)
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 2010
Series:Cambridge series on statistical and probabilistic mathematics
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
LEADER 01928nmm a2200277 u 4500
001 EB001819824
003 EBX01000000000000000986270
005 00000000000000.0
007 cr|||||||||||||||||||||
008 180505 ||| eng
020 |a 9780511750489 
050 4 |a QA274.75 
100 1 |a Mörters, Peter 
245 0 0 |a Brownian motion  |c Peter Mörters and Yuval Peres ; with an appendix by Oded Schramm and Wendelin Werner 
260 |a Cambridge  |b Cambridge University Press  |c 2010 
300 |a xii, 403 pages  |b digital 
653 |a Brownian motion processes 
700 1 |a Peres, Y.  |e [author] 
700 1 |a Schramm, Oded  |e [author] 
700 1 |a Werner, Wendelin  |e [author] 
041 0 7 |a eng  |2 ISO 639-2 
989 |b CBO  |a Cambridge Books Online 
490 0 |a Cambridge series on statistical and probabilistic mathematics 
856 4 0 |u https://doi.org/10.1017/CBO9780511750489  |x Verlag  |3 Volltext 
082 0 |a 530.475 
520 |a 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