Stochastic analysis on manifolds
Collection : Graduate studies in mathematics. Publié par : American Mathematical Society ([S.l.]) Détails physiques : 281 p. 27 cm. ISBN :0821808028 (hardcover); 9780821808023 (hardcover). Année : 2002Type de document | Site actuel | Cote | Statut | Date de retour prévue | Code à barres | Réservations |
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Livre | La bibliothèque des Sciences Exactes et Naturelles | 519.2 HSU (Parcourir l'étagère) | Disponible | 0000000019646 |
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.
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