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Elton P. Hsu 作者

American Mathematical Society

译者

February 5, 2002 出版日期

281 pages 页数

$48.00 价格

Hardcover

Graduate Studies in Mathematics 丛书系列

9780821808023 图书编码

Stochastic Analysis on Manifolds 在线电子书图书标签: on Stochastic Manifolds Analysis

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Stochastic Analysis on Manifolds 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Stochastic Analysis on Manifolds 在线电子书图书描述

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-Chern 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.

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