Elton Hsu
Northwestern University
Title: Brownian Motion on Manifolds, Heat Kernel, and the Cameron-Martin Theorem
Abstract: The Laplace-Beltrami operator generates a diffusion process on the path space over a Riemannian manifold. This process, called Riemannian Brownian motion is the main object of study in stochastic analysis on manifolds. In this talk, we will survey two recent results in stochastic analysis. In the first problem, we study the escape rate of Brownian motion on a complete Riemannian manifold and give a fairly precise rate of growth of Brownian motion in terms of the volume growth of the manifold. In the second problem, we generalize the classical Cameron-Martin theorem on the quasi-invariance of Euclidean Brownian motion under a shift. A common feature of these two results is that they hold on a general geometrically complete Riemannian manifold.
This is a joint work with Guang Nan Qin of Institute of Applied Mathematics of the Chinese Academy of Sciences and Cheng Ouyang of Purdue University.
©2010, Department of Mathematical Sciences
Last Modified: February 26, 2009