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Brownian motion

By: Contributor(s): Series: Cambridge series in statistical and probabilistic mathematics, 30Publication details: 2010 Cambridge University Press New YorkDescription: xii, 403 pISBN:
  • 9780521168847
Subject(s): DDC classification:
  • 530.475 M6B7
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.
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 33-A / Slot 1699 (2nd Floor, East Wing) Non-fiction General Stacks 530.475 M6B7 (Browse shelf(Opens below)) Available 178307

Includes bibliographical references (p. 386-399) and index.

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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