Potential Theory of Subordinate Brownian Motions
主 题: Potential Theory of Subordinate Brownian Motions
报告人: Professor Renming Song ) (University of Illinois at Urbana-Champaign)
时 间: 2016-05-27 15：00-16：00
地 点: 理科一号楼 1114（数学所活动）
A subordinate Brownian motion can be obtained by replacing the time parameter of a Brownian motion by an independent increasing Levy process(i. e., a subordinator). Subordinate Brownian motions form a large subclass of Levy processes and they are very important in various applications. The generator of of a subordinate Brownian motion is a function of the Laplacian. In this talk, I will give a survey of some of the recent results in the study of the potential theory of subordinate Brownian motions. In particular, I will present recent results on sharp two-sided estimates on the transition densities of killed subordinate Brownian motions in smooth open sets, or equivalently, sharp two-sided estimates on the Dirichlet heat kernels of the generators of subordinate Brownian motions.