Prof. Zhen-Qing Chen : Brownian Motion on Spaces with Varying Dimension

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

At

April 24, 2013, 4 p.m.

In

SEO 636

Abstract

Image an insect moves randomly in a plane with an infinite pole installed on it. In this talk, we will introduce and discuss Brownian motion on a state space with varying dimension. We will derive sharp two-sided estimates on its transition density function (also called heat kernel). The two-sided estimates is of Guassian type but the parabolic Harnack inequality fails for such process and the measure on the underlying state space does not satisfy volume doubling property.