Description

Book Synopsis
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.

Table of Contents
Introduction Stochastic differential equations and diffusions Basic stochastic differential geometry Brownian motion on manifolds Brownian motion and heat kernel Short-time asymptotics Further applications Brownian motion and analytic index theorems Analysis on path spaces Notes and comments General notations Bibliography Index.

Stochastic Analysis on Manifolds

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      Publisher: American Mathematical Society
      Publication Date: Publication Date: 28/02/2002
      ISBN13: 9780821808023, 978-0821808023
      ISBN10: 0821808028

      Description

      Book Synopsis
      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.

      Table of Contents
      Introduction Stochastic differential equations and diffusions Basic stochastic differential geometry Brownian motion on manifolds Brownian motion and heat kernel Short-time asymptotics Further applications Brownian motion and analytic index theorems Analysis on path spaces Notes and comments General notations Bibliography Index.

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