一、题目：

Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes

二、主讲人：

邵井海

三、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, an 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.

四、主讲人简介：

邵井海，天津大学应用数学中心教授，博士生导师。2006年获得北京师范大学与法国第戎大学的理学博士学位。邵井海主要从事概率论遍历性理论、随机分析、随机微分方程方面的研究工作，在轨道空间和环空间上运输不等式、Monge-Kantorovich最优映射问题，以及带切换扩散过程长时间行为等问题的研究中取得了一些成果。

五、邀请人：

陈章

六、时间：

12月8日（周四）19:30-21:00

七、地点：

腾讯会议

八、联系人：

张亚辉，联系方式：yahzhang@mail.sdu.edu.cn

九、主办：

山东大学数学学院