Convergence,boundedness,and ergodicity of regime-switching diusion processes with infinite memory

作     者：Jun LI Fubao XI Jun LI;Fubao XI

作者机构：School of Mathematics and StatisticsBeijing Institute of TechnologyBeijing 100081China Department of Applied MathematicsLanzhou University of TechnologyLanzhou 730050China Beijing Key Laboratory on MCAACIBeijing Institute of TechnologyBeijing 100081China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2021年第16卷第2期

页      面：499-523页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant No.12071031) 

主　　题：Regime-switching diffusion process infinite memory convergence boundedness Feller property invariant measure Wasserstein distance 

摘      要：We study a class of diffusion processes, which are determined by solutions X(t) to stochastic functional differential equation with infinite memory and random switching represented by Markov chain Λ(t): Under suitable conditions, we investigate convergence and boundedness of both the solutions X(t) and the functional solutions Xt: We show that two solutions (resp., functional solutions) from different initial data living in the same initial switching regime will be close with high probability as time variable tends to infinity, and that the solutions (resp., functional solutions) are uniformly bounded in the mean square sense. Moreover, we prove existence and uniqueness of the invariant probability measure of two-component Markov-Feller process (Xt,Λ(t));and establish exponential bounds on the rate of convergence to the invariant probability measure under Wasserstein distance. Finally, we provide a concrete example to illustrate our main results.