Description
Book SynopsisProbability theory has become a convenient language and a useful tool in many areas of modern analysis. This book intends to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. It begins with a review of stochastic differential equations on Euclidean space.
Table of ContentsIntroduction Stochastic differential equations and diffusions Basic stochastic differential geometry Brownian motion on manifolds Brownian motion and heat kernel Short-time asymptotics Further applications Brownian motion and analytic index theorems Analysis on path spaces Notes and comments General notations Bibliography Index.
