Variational formula for the stability of regime-switching diffusion processes

作     者：Jinghai Shao Lingdi Wang 

作者机构：Center for Applied Mathematics Tianjin University School of Mathematics and Statistics Henan University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第4期

页      面：659-676页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11301030, 11401169 and 11431014) Key Scientific Research Projects of Henan Province (Grant No. 16A110010) 

主　　题：stability in probability regime switching diffusions state dependent M matrix 

摘      要：The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coefficients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.