Probability Seminar —— Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary
报告人：宋仁明 （University of Illinois Urbana-Champaign）
时间：2026-04-27 14:00-15:00
地点：四元厅
Abstract: In this talk, I will present some recent results about purely discontinuous symmetric Markov processes on closed subsets of ${\mathbb R}^d$, $d\ge 1$, with jump kernels of the form $J(x,y)=|x-y|^{-d-\alpha}{\mathcal B}(x,y)$, $\alpha\in (0,2)$, where the function ${\mathcal B}(x,y)$ may blow up at the boundary of the state space.
We study both conservative Markov processes of this type and critically killed Markov processes of this type. Examples of Markov processes that fall into our general framework include traces of isotropic $\alpha$-stable processes in $C^{1,\rm Dini}$ sets, processes in Lipschitz sets arising in connection with the nonlocal Neumann problem, and a large class of resurrected self-similar processes in the closed upper half-space. Our main results are sharp two-sided heat kernel estimates for these Markov processes. This talk is based on joint works with Soobin Cho, Panki Kim and Zoran Vondracek.
Bio: Renming got his PhD in 1993 from the University of Florida. He joined the Mathematics Department of the University of Illinois Urbana-Champaign in 1997. His main interest is in Markov process, potential theory and branching processes.
