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Item Details
Title:
STOCHASTIC ANALYSIS ON MANIFOLDS
By:
Elton P. Hsu
Format:
Hardback
List price:
£91.00
Our price:
£88.27
Discount:
3
% off
You save:
£2.73
ISBN 10:
0821808028
ISBN 13:
9780821808023
Availability:
Usually dispatched within 3-5 days.
Delivery rates
Stock:
Currently
1
item in stock
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:
US
Imprint:
American Mathematical Society
Returns:
Returnable
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