Boundary Behaviors at $\infty$ for Fragments in Simple Exchangeable Fragmentation-Coalescence Processes

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:Xiaowen Zhou
:2021-08-27 08:00
:腾讯会议 ID: 947 842 339(无密码)

报告人:Xiaowen ZhouConcordia University


  点:腾讯会议 ID 947 842 339(无密码)


Exchangeable fragmentation-coagulation (EFC) processes are partition-valued stochastic processes first introduced by Berestycki. In this talk we consider the EFC processes for which the coagulations are multiple and not simultaneous, as in a $\Lambda$-coalescent, and the fragmentations dislocate at finite rate an individual block into sub-blocks of infinite size. Sufficient conditions are found for the block counting process to explode (i.e. to reach $\infty$) or not and for $\infty$ to be either an exit boundary or an entrance boundary. In a case of regularly varying fragmentation and coagulation mechanisms, we find regimes where the boundary $\infty$ can be either an exit, an entrance or a regular boundary. (This talk is based on joint work with Clement Foucart.)


周晓文,晓文教授, 1999年在美国加州大学Berkeley分校获统计学博士学位。现任加拿大Concordia大学数学与统计系终身教授。长期从事概率论与随机过程理论的研究,主要研究兴趣包括测度值随机过程,勒维过程及其在种群遗传学和风险理论中的应用。先后在《Annals of Probability》、《Probability Theory and Related Fields》、《Annals of Applied Probability》等国际顶级概率刊物发表论文60余篇。