Stochastic Analysis on Manifolds pdf epub mobi txt 電子書 下載 2024


Stochastic Analysis on Manifolds

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Elton P. Hsu
American Mathematical Society
February 5, 2002
281 pages
$48.00
Hardcover
Graduate Studies in Mathematics
9780821808023

圖書標籤: on  Stochastic  Manifolds  Analysis   


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发表于2024-11-23

Stochastic Analysis on Manifolds epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

Stochastic Analysis on Manifolds epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024

Stochastic Analysis on Manifolds pdf epub mobi txt 電子書 下載 2024



圖書描述

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.

Stochastic Analysis on Manifolds 下載 mobi epub pdf txt 電子書

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Stochastic Analysis on Manifolds pdf epub mobi txt 電子書 下載
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