Variational formula for the stability of regime-switching diffusion processes  

作　　者：Jinghai Shao Lingdi Wang 

机构地区：[1]Center for Applied Mathematics, Tianjin University [2]School of Mathematics and Statistics, Henan University

出　　处：《Science China Mathematics》2018年第4期659-676,共18页中国科学：数学（英文版）

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)

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.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.

关 键 词：stability in probability regime-switching diffusions state-dependent M-matrix 

分 类 号：O175[理学—数学]