10月13日 江苏高校优势学科概率统计前沿系列讲座之一百一十一

发布时间:2018-10-09浏览次数:11

报 告 人:张希承 教授

报告题目:Dirichlet problem for supercritical non-local operators

报告时间:2018年10月13日(周六)上午10:40

报告地点:金晨假日酒店正德厅

报告人简介:

  张希承,武汉大学数学与统计学院教授,博士生导师。2001.09-2002.09,葡萄牙里斯本大学博士后,其中于2002年2月受法国科学院院士Malliavin邀请访问巴黎六大。2004.02-2004.08,法国La Rochelle大学博士后。2006.02-2007.06,德国洪堡奖学金资助于德国Bielefeld大学从事随机分析研究。2007.06-2009.06,澳大利亚新南威尔士大学博士后。2010年入选教育部“新世纪优秀人才支持计划,先后主持国家自然科学基金项目4项,2013年获国家自然科学基金杰出青年项目。2016年获教育部 “长江学者”特聘教授。迄今,他已在概率和方程方向的顶级刊物Annals of Probability,Probability Theory and Related Fields,Stochastic Processes and their Applications,Journal of Functional Analysis,Journal of Differential Equation,Potential Analysis,Annals of Applied Probability,Communications in Mathematical Physics等期刊上发表论文一百多余篇,研究深度和广度在获得国内外一定的认可。

报告摘要:

  Let D be a bounded -domain. Consider the following Dirichlet initial-boundary problem of nonlocal operators with a drift:

in

Where and is an -stable-like nonlocal operator with kernel function bounded from above and below by positive constants, and is a bounded -function with is a -function in D uniformly in t with Under some HÖlder assumptions on , we show the existence of a unique classical solution to the above problem. Moreover, we establish the following probabilistic representation for

where  is the Markov process associated with the operator and is the first exit time of X from D.  In the sub and critical case, the kernel function can be rough in z.  In the supercritical case , we classify the boundary points according to the sign of where and is the unit outward normal vector.  Finally, we provide an example and simulate it by Monte-Carlo method to show our results.