Stochastic Analysis on Manifolds PDF
by Elton P Hsu
Description
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.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:281 pages
- Publisher:American Mathematical Society
- Publication Date:02/01/2015
- Category:
- ISBN:9781470420901
Information
-
Download - Immediately Available
- Format:PDF
- Pages:281 pages
- Publisher:American Mathematical Society
- Publication Date:02/01/2015
- Category:
- ISBN:9781470420901
