Open AccessExponential ergodicity for regime-switching diffusion processes in total variation norm
Author(s) -
Jun Li,
Fu Xi
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021309
Subject(s) - ergodicity , uniqueness , mathematics , invariant measure , exponential function , norm (philosophy) , probability measure , invariant (physics) , exponential growth , measure (data warehouse) , statistical physics , ergodic theory , mathematical analysis , statistics , physics , computer science , mathematical physics , database , political science , law
We investigate the long time behavior for a class of regime-switching diffusion processes. Based on direct evaluation of moments and exponential functionals of hitting time of the underlying process, we adopt coupling method to obtain existence and uniqueness of the invariant probability measure and establish explicit exponential bounds for the rate of convergence to the invariant probability measure in total variation norm. In addition, we provide some concrete examples to illustrate our main results which reveal impact of random switching on stochastic stability and convergence rate of the system.