02288nam a22003498a 4500 CR9780511750489 UkCbUP 20180107143412.0 m|||||o||d|||||||| cr|||||||||||| 100412s2010||||enk s ||1 0|eng|d 9780511750489 (ebook) 9780521760188 (hardback) UkCbUP UkCbUP rda QA274.75 .M67 2010 530.4/75 22 Mörters, Peter, author. Brownian Motion / [electronic resource] Peter Mörters, Yuval Peres. Cambridge : Cambridge University Press, 2010. 1 online resource (416 pages) : digital, PDF file(s). text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge Series in Statistical and Probabilistic Mathematics ; no. 30 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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. Brownian motion processes Peres, Yuval, author. Print version: 9780521760188 Cambridge Series in Statistical and Probabilistic Mathematics ; no. 30. http://dx.doi.org/10.1017/CBO9780511750489 Cambridge Books Online 236499 236499