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Stochastic Analysis on Manifolds (Graduate Studies in Mathematics): No. 38

Applied Mathematics

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Description

Probability theory has become a convenient language and a useful tool in many areas of modern analysis. The main purpose of this book is to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A dominant theme of the book is the probabilistic interpretation of the curvature of a manifold.The book begins with a brief review of stochastic differential equations on Euclidean space. After presenting the basics of stochastic analysis on manifolds, the author introduces Brownian motion on a Riemannian manifold and studies the effect of curvature on its behavior. He then applies Brownian motion to geometric problems and vice versa, using many well-known examples, e.g., short-time behavior of the heat kernel on a manifold and probabilistic proofs of the Gauss-Bonnet-Chem theorem and the Atiyah-Singer index theorem for Dirac operators. The book concludes with an introduction to stochastic analysis on the path space over a Riemannian manifold.

Product Specifications

Format: hardcover
ASIN: 0821808028
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Applied Mathematics
Domain: Amazon UK
Release Date: 28 March 2002
Listed Since: 17 December 2006

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Stochastic Analysis on Manifolds (Graduate Studies in Mathematics): No. 38

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