报告问题 (Title)： Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes（带切换扩散历程的较量定理及转移速率矩阵扰动下的稳固性）

报告人 (Speaker)： 邵井海 教授（天津大学）

报告时间 (Time)：2022年6月4日 (周六) 10:00-12:00

报告所在 (Place)：腾讯聚会（聚会号：103-628-251 无密码）

约请人(Inviter)：阳芬芬

主理部分：理学院数学系

报告摘要：A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to control pathwisely the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on the elaborate constructions of switching processes in the spirit of Skorokhod's representation theorem varying according to the problem being dealt with. In particular, this method can cope with the switching processes in an infinite state space and not necessarily being of birth-death type. As an application, some known results on ergodicity and stability of state-dependent regime-switching processes can be improved.