STOCHASTIC ANALYSIS ON MANIFOLDS by Elton P. Hsu ( 9780821808023 )

Item Details

Title:

STOCHASTIC ANALYSIS ON MANIFOLDS

By:

Elton P. Hsu

Format:

Hardback

List price:

£85.00

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£82.45

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£2.55

ISBN 10:

0821808028

ISBN 13:

9780821808023

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Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

1 February, 2002

Series:

Graduate Studies in Mathematics No. 38

Pages:

273

Description:

Probability theory has become a convenient language and a useful tool in many areas of modern analysis. This book intends to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. It begins with a review of stochastic differential equations on Euclidean space.

Synopsis:

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.

Illustrations:

bibliography, index

Publication:

Imprint:

American Mathematical Society

Returns:

Returnable

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