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Brownian motion

By: Morters, Peter.
Contributor(s): Peres, Yuval.
Series: Cambridge series in statistical and probabilistic mathematics / edited by Z. Ghahramani. Publisher: Cambridge Cambridge University Press 2010Description: xii, 403p.ISBN: 9780521760188.Subject(s): Motion -- MathematicsDDC classification: 530.475 | M842b Summary: 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.
List(s) this item appears in: New Arrival Nov.12th - 18th, 2018
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Item type Current location Collection Call number url Status Date due Barcode Item holds
Books Books PK Kelkar Library, IIT Kanpur
TEXT 530.475 M842b (Browse shelf) Checked out to PRANAY AGARWAL (S1981762300) 06/03/2024 A183976
Total holds: 0

with an appendix by Oded Schramm and Wendelin Werner

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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