Prof. Elton P Hsu : How fast does a Brownian motion move on a manifold?

Posted by , part of the Statistics and Data Science Seminar.

At

Nov. 12, 2008, 4:15 p.m.

In

SEO 612

Abstract

How fast does a transient Brownian motion escape to infinity is an interesting question. For example, it is well known that Brownian motion in a euclidean space of dimension 3 and higher escapes to infinity at approximately the rate of the square root of time. Which geometric quantity controls the rate of escape is an interesting question. We will explain that the speed of Brownian motion can be effectively controlled by the volume growth rate of a complete Riemannian manifold. A precise integral criterion is obtained which in many cases is sharp.