概率统计系列讲座五：
报告题目【Recent Studies on Sample Functions of Levy and Levy-Type Processes】
时间：2020年9月19日 (星期六) 上午09:00
地点：腾讯会议（ID 511 3889 6273）
主讲：美国密西根州立大学教授，肖益民
主办：数学与信息学院
参加对象：统计系老师与学生
报告摘要：Sample path properties of Levy processes and more general Markov processes have been studied for a long time. Many authors have studied their fractal properties and potential theory and established many important results. This talk will focus on recent progress in the studies of Levy and Levy-type processes.
For Levy processes, we present some recent results along the following two lines of research:
(i) By establishing potential-theoretical results for additive Levy processes, Khoshnevisan and Xiao (2002 -) have
developed some new ways to study Hausdorff and packing dimensions of various random sets generated by Levy
processes.
(ii) By exploring the connection between localof symmetric Levy processes and Gaussian processes established
by Dynkin's Isomorphism Theorems, Marcus and Rosen (1992 -) have studied in-depth the regularity properties of local tomes of Levy processes. For non-symmetric Levy processes, the role of Gaussian processes is replaced
by the permanental processes whose studies are still at an early stage.
For Levy-type processes, including stable-like processes, stable jump diffusions, Feller processes associated with
pseudo-differential operators, and solutions of SDEs driven by Levy noises, research along the lines of (i) and (ii)
would be very fruitful but remains to be almost unexplored. If time permits, I will mention some recent results on
favorite points of Levy processes (Li, Xiao, and Yang, 2019), and fractal dimensions of Levy-type processes including
the uniform dimension results obtained in Sun, Xiao, Xu and Zhai (2018), and Park, Xiao, and Yang (2020).
