Stochastic Analysis on Manifolds - Couverture rigide

Hsu, Elton P.

Couverture rigide

ISBN 10 : 0821808028 ISBN 13 : 9780821808023

Editeur : American Mathematical Society, 2002

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2002
• Langue: anglais
• ISBN 10: 0821808028
• ISBN 13: 9780821808023
• Reliure: Relié
• Nombre de pages: 281
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible