Exponential Ergodicity of Branching Processeswith Immigration and Competition

Speaker: Zenghu Li (Beijing Normal University)

Date: May 17 Tues. 4:00pm

Venue: Tencent Meeting Room: 750 581 912

Abstract: 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. (Probab. Theory Relat. Fields, 2018) with an additional immigration structure. The exponential ergodicity in a weighted total variation distance is proved for such a process with general branching mechanism including all stable cases. The proof is based on a Markov coupling process and a non-symmetric control function for the distance. which are designed to identify and to take advantage of the dominating factor among the branching. immigration and competition mechanisms in different parts of the state space. The main result is applied to two typical choices of the distance.

This is a joint work with Peisen Li, Jian Wang and Xiaowen Zhou.