报 告 人：宋仁明 教授
报告题目：Trace estimates for relativistic stable processes
报告时间：
报告地点：静远楼1506学术报告厅
报告摘要：The trace asymptotics of killed Brownian motions (or Dirichlet Laplacians) in bounded domains have been well studied. Recently, Banuelos and his collaborators studied the trace asymptotics of killed symmetric stable processes (or Dirichlet fractional Laplacians) in bounded domains. In this talk I will present some recent results on the trace asymptotics of killed relativistic a- stable processes in bounded domains. The results include asymptotics expansions of the trace in terms of the time parameter t with an error bound of order t(2-d)^a for C(1,1) open sets and of order t(2-d)^a for Lipschitz open sets. Compared with the corresponding expansions for a-stable processes, there are more terms between the orders t(2-d)^a and t(2-d)^a for C(1,1) open sets, and, when a(0,1], between the orders t(2-d)^a and t(2-d)^a for Lipschitz open sets.
宋仁明教授简介：
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。