000			01689 a2200229 4500
005			20181114153933.0
008			181114b xxu||||| |||| 00| 0 eng d
020			_a9780521760188
040			_cIIT Kanpur
041			_aeng
082			_a530.475 _bM842b
100			_aMorters, Peter
245			_aBrownian motion _cPeter Morters and Yuval Peres
260			_bCambridge University Press _c2010 _aCambridge
300			_axii, 403p
440			_aCambridge series in statistical and probabilistic mathematics / edited by Z. Ghahramani
500			_awith an appendix by Oded Schramm and Wendelin Werner
520			_aThis 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.
650			_aMotion -- Mathematics
700			_aPeres, Yuval
942			_cBK
999			_c559536 _d559536