Stochastic Analysis on Manifolds Hardback
Part of the Graduate Studies in Mathematics series
Hardback
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-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.
Information
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Only a few left - usually despatched within 24 hours
- Format:Hardback
- Pages:bibliography, index
- Publisher:American Mathematical Society
- Publication Date:28/02/2002
- Category:
- ISBN:9780821808023
Other Formats
- PDF from £47.70
Information
-
Only a few left - usually despatched within 24 hours
- Format:Hardback
- Pages:bibliography, index
- Publisher:American Mathematical Society
- Publication Date:28/02/2002
- Category:
- ISBN:9780821808023
