Stochastic analysis on manifolds hsu pdf file

Hsu department of mathematics, northwestern university. Functional analysis mostly operator theory and operator algebras. Lecture notes in mathematics 851, 1981, nelson, 1985, schwartz, 1984. This geometric insight further promoted the integration of tools from stochastic analysis on manifolds 29, 52 into the context of mathematical finance. In this article, we present the theoretical basis for an approach to steins method for probability distributions on riemannian manifolds. Stochastic di erential equations on manifolds hsu, chapter 1. A brief introduction to brownian motion on a riemannian manifold elton p. A key theme is the probabilistic interpretation of the curvature of a manifold. An introduction to stochastic analysis on manifolds i. Horizontal lift and stochastic development hsu, sections 2. Mathematische forschungsinstitut oberwolfach report 54 2005, 3234. These lecture notes constitute a brief introduction to stochastic analysis on manifolds in general, and brownian motion on riemannian manifolds in particular.