Brownian Motion on Spaces with Varying Dimensions
Professor Zhen-Qing Chen
University of Washington and Beijing Institute of Technology报告时间：2013年6月19日（星期三）,下午16:00—17:00报告地点：北航数学与系统科学ag平台app下载主213学术交流厅报告摘要：
Brownian motion is a building block of modern probability theory. It has important and intrinsic connections to analysis and partial differential equations as the infinitesima generator of Brownian motion is the Laplace operator. 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 (or equivalently, ``Laplace operator") on a state space with varying dimension. I will present sharp two-sided estimates on its transition density function (also called heat kernel). The two-sided estimates are 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.
Zhen-Qing Chen received his Ph.D in mathematics from Washington University in St. Louis in 1992. After working at the University of California at San Diego and Cornell University, he joined the University of Washington in 1998, where he has been a Professor of Mathematics since 2003. His research interests include stochastic analysis, Markov processes, Dirichlet form theory and their applications. He is an elected Fellow of the Institute of Mathematical Statistics. In 2008, he was named a ChangJiang Chair Professor at the Beijing Institute of Technology by the Chinese Ministry of Education. He serves as an associate editor for The Annals of Applied Probability, The Annals of Probability, Stochastic Processes and their Applications, and as an editorial board member for Journal of Theoretical Probability, Potential Analysis, and Science China Mathematics.