报告题目：Exponential ergodicity of branching processes with immigration and competition

报告人：Zenghu Li (Beijing Normal University)

报告时间：3月30日  10:00

报告地点：Zoom 94876249246 密码 002585

摘要：We study the ergodic property of a continuous-state branching process with immigration and competition, which is an extension of the models introduced by Pardoux (2016, Springer) and Berestycki et al. (2018, Probably. Theory Relat. Fields) with an additional immigration structure. The process is constructed by the pathwise unique nonnegative solution to a stochastic equation driven by time-space Levy noises. The immigration and competition structures make it possible for us to obtain exponential convergence rates in weighted total variation distances to the non-degenerate stationary distribution for general branching mechanisms. The results apply in particular to all stable branching mechanisms. The proof of the exponential ergodicity is based on the construction of a Markov coupling of the process and the choice of a non-symmetric control function for the distance. This is a joint work with Peisen Li, Jian Wang and Xiaowen Zhou.