Continuous-state Nonlinear Branching Processes
题目：Continuous-state Nonlinear Branching Processes
报告人：周晓文 教授 (加拿大Concordia大学)
时间：2022年11月3日（周四）9:00-10:00
地点：腾讯会议 会议ID：889-344-185（1103）
会议链接：https://meeting.tencent.com/dm/kCM1X1DJoNYJ
摘要：
Continuous-state branching processes can be treated as continuous-state counterparts of discrete-state Bienaym´e-Galton-Watson processes. We consider a class of continuous-state branching processes with branching rates depending on the current population sizes. They are nonnegative-valued Markov processes that can be obtained either from spectrally positive L´evy processes via Lamperti type time changes or as unique solutions to SDEs driven by Brownian motion and (or) Poisson random measure with positive jumps. The nonlinear branching mechanism allows the processes to have exotic behaviours such as coming down from infinity. But at the same time it brings new challenges to their study for lack of the additive branching property.
In this talk we mainly introduce the above continuous-state nonlinear branching processes. We also present recent results on the coming down from infinity, the explosion and the extinguishing behaviours for such processes. It is based on joint work with Clement Foucart, Bo Li, Junping Li, Pei-Sen Li and Yingchun Tang.
专家简介：
周晓文，1997年博士毕业于美国加州大学伯克利分校，现为加拿大Concordia大学数学与统计系终身教授，主要研究兴趣包括测度值随机过程，Levy过程及其在种群遗传学和风险理论中的应用，周晓文教授长期从事概率论与随机过程理论的研究，特别是在超过程和Levy过程及风险模型等方面，解决或部分解决了著名概率论专家Donald Dawson，Steven Evans，Ian Iscoe，Luis Gorostiza等人提出的问题或猜想。在Annals of Probability，Probability Theory and Related Fields, Annals of Applied Probability, Electronic Journal of Probability, Ann. Inst. Henri Poincaré Probab. Stat., Stochastic Processes and Their Applications，Journal of Applied Probability，Journal of Differential Equations，Insurance Mathematics & Economics等重要杂志上发表论文70余篇。
