A seminar at Center for Mathematical Sciences, July 30, Thursday, at 4:00pm
Location：Center for Mathematical Sciences, Room 813（创新研究院恩明楼813室）
Speaker: Zhen-Qing Chen, University of Washington
Title: Heat kernels for non-local operators
Abstract: Transition density function encodes all the information about a Markov process. It is the fundamental solution (also called heat kernel) of the infinitesimal generator of the corresponding Markov process.When the Markov process is a diffusion on Euclidean space, its infinitesimal generator is a differential operator. When the Markov process has discontinuous sample paths, its infinitesimal generator is a non-local operator. Heat kernels for second order elliptic operators have been well studied and there are many beautiful results. The study of heat kernels for non-local operators is quite recent. In this talk, I will survey the recent progress in the study of heat kernels of non-local operators, focusing on their two-sided estimates, stability, and their applications to solutions of stochastic differential equations driven by Levy processes.