Cylindrical stable processes

活动时间:2022-12-04 10:00

活动地点:腾讯会议 353-2841-3637



陈振庆教授,是国际顶级期刊《The Annals of Probability》的副主编,国际顶级期刊《Potential Analysis》和《Proceedings of the American Mathematical Society》的主编,《中国科学》等众多期刊的编委。 陈振庆教授,1992年在美国华盛顿大学(圣路易斯)获博士学位,曾在美国的加利福尼亚大学(圣地亚哥)和康奈尔大学工作;1998年起在位于华盛顿州西雅图市的华盛顿大学数学系工作至今。主要从事概率论及随机过程的研究,主要研究方向是:随机分析,随机微分方程,马氏过程及其位势理论,狄氏型,发表论文150余篇。


A cylindrical \alpha-stable process on R^d is a Levy process whose coordinate processes are independent copies of one-dimensional \alpha-stable processes. They have many distinct properties from that of isotropic stable processes. In this talk, I will first present a geometric characterization of an open subset so that the part process X^D of X killed upon leaving D is irreducible, and show that this is equivalent to the strict positivity of its transition density function p_D(t, x, y). I will then present results on the  properties of p_D(t, x, y) including its regularity as well as its sharp two-sided bounds for C^{1,1} open set D. Our bounds are shown to be sharp for a class of C^{1,1} open sets.