Exponential ergodicity for regime-switching diffusion processes in total variation norm

Jun Li; Fubao Xi

doi:10.3934/dcdsb.2021309

Article Contents

2022, Volume 27, Issue 10: 6125-6146. Doi: 10.3934/dcdsb.2021309

This issue Previous Article Emergent behaviors of discrete Lohe aggregation flows Next Article Multi-valued random dynamics of stochastic wave equations with infinite delays

Exponential ergodicity for regime-switching diffusion processes in total variation norm

Jun Li^1,2, and
Fubao Xi^1, ,

1.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2.
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

^* Corresponding author: Fubao Xi
^* Corresponding author: Fubao Xi

Received: July 2021

Revised: November 2021

Early access: January 2022

Published: October 2022

The research was supported by the National Natural Science Foundation of China (12071031)

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Abstract

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.

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Mathematics Subject Classification: Primary: 60H10, 60J60; Secondary: 60K37.

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