报 告 人：宋仁明 教授（伊利诺伊大学）
报告题目：Potential theory of subordinate killed Brownian motions
报告时间：2016年10月20日（周四）下午2:30
报告地点：静远楼1506报告厅
报告摘要： Let 
be a killed Brownian motion in a domain 
and 
an independent subordinator with Laplace exponent 
. The process 
defined by 
is called a subordinate killed Brownian motion. It is a Hunt process with infinitesimal generator 
, where 
is the Dirichlet Laplacian. In this talk I will present several recent potential theoretic results for 
under a weak scaling condition on the derivative of 
. These results include the scale invariant Harnack inequality for nonnegative harmonic functions of 
, and two types of scale invariant boundary Harnack principle with explicit decay rates. The first boundary Harnack principle deals with a 
domain 
and non-negative functions which are harmonic near the boundary of 
, while the second one is for a more general domain 
and non-negative functions which are harmonic near the boundary of an interior open subset of 
. The obtained decay rates are not the same, reflecting different boundary and interior behaviors of 
. The results are new even in the case of a stable subordinator.
This talk is based on a joint paper with Panki Kim and Zoran Vondracek.
报告人简介：
宋仁明，伊利诺伊大学数学系教授，主要从事随机分析和马氏过程的研究。1979年考入河北大学数学系，1983年和1986年分别获得学士和硕士学位；1993年毕业于佛罗里达大学数学系，获博士学位；1993年至1994年为美国西北大学数学系访问助理教授；1994年至1997年为密西根大学数学系助理教授；1997年进入伊利诺伊大学数学系。在Ann. Probability, Probab. Theory Related Fields , Math. Ann, J. Eur. Math. Soc. , J. Funct. Anal. , Proc. Lond. Math. Soc. , T Trans. Amer. Math. Soc. , Stochastic Process. Appl. 等数学和概率论Top杂志上发表论文100多篇，出版专著2部。