欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
学术信息
SEMINARS
On the potential theory of jump processes in open sets
时间  Datetime
2019-08-16 16:00 — 17:00 
地点  Venue
Middle Lecture Room(703)
报告人  Speaker
Panki Kim
单位  Affiliation
Seoul National University
邀请人  Host
陈昕
报告摘要  Abstract

Consider a $\beta$-stable process in the Euclidean space, which is killed upon exiting an open subset $D$. The killed process is then subordinated via an independent $\gamma$-stable subordinator. The resulting process $Y^D$ is called a subordinate killed stable process. In two recent papers, it has been shown that the potential theory of this process exhibits some interesting features. The first one is the form of the jumping kernel which depends on the distance of points to the boundary in a novel way. The second and unexpected feature is the fact that for some values of the stability index $\gamma$, the boundary Harnack principle fails. In the first part of the talk, I will review these results. The second part of the talk will be devoted to ongoing work on potential theory of jump processes in open subset $D$ defined through their jumping kernels that depend not only on the distance between two points, but also on the distance of each point to the boundary of the state space $D$. Joint work with Zoran Vondracek and Renming Song.