Stochastic Analysis on Manifolds - Rilegato

Hsu, Elton P.

Rilegato

ISBN 10: 0821808028 ISBN 13: 9780821808023

Casa editrice: Amer Mathematical Society, 2002

Riassunto

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.

Su questo libro

Product Description:

Book by Hsu Elton P

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2002
• ISBN 10: 0821808028
• ISBN 13: 9780821808023
• Rilegatura: Copertina rigida
• Numero di pagine: 281