## Brownian Motion on Spaces with Varying Dimension

**报告题目****: **Brownian Motion on Spaces with Varying Dimension.

**报告人****:** Prof. Zheng-Qing Chen，Department of Mathematics，University of Washington，Seattle, USA.

**时间****:** 2013年6月14日（星期五）16:00-17:00

**地点****:** 理科楼数学系A404

**摘要****:** Brownian motion is a building block of modern probability theory.It has important and intrinsic connections to analysis and partial differential equations.In real world, there are many examples of spaces with varying dimensions. For example, image an insect moves randomly in a plane with an infinite pole installed on it.In this talk,I will introduce and discuss Brownian motion on a state space with varying dimension, as well as its infinitesimal generator. I will present 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.

**联系人****:** 胡家信