Abstract: 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 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.
Bio: Prof. Renming Song got his PhD from the University of Florida in 1993. He is now a professor of Mathematics at the University of Illinois at Urbana-Champaign. His main research interests are Markov processes, stochastic analysis, potential theory and branching processes.
