Curved Wiener Space Analysis

Abstract

These notes represent a much expanded and updated version of the \textquotedblleft mini course\textquotedblright that the author gave at the ETH (Z\"{u}rich) and the University of Z\"{u}rich in February of 1995. The purpose of these notes is to first provide some basic background to Riemannian geometry and stochastic calculus on manifolds and then to cover some of the more recent developments pertaining to analysis on \textquotedblleft curved Wiener spaces.\textquotedblright Essentially no differential geometry is assumed. However, it is assumed that the reader is comfortable with stochastic calculus and differential equations on Euclidean spaces.