On subgeometric ergodicity of regime-switching diffusion processes

TL;DR

This paper investigates conditions under which regime-switching diffusion processes exhibit subgeometric ergodicity, providing criteria related to drift, diffusion, and switching mechanisms, including processes with jumps.

Contribution

It establishes new conditions for subgeometric ergodicity of regime-switching diffusions and extends results to processes with jumps, enriching the theoretical understanding of their long-term behavior.

Findings

Derived conditions for subgeometric ergodicity based on drift and diffusion coefficients.

Established ergodicity results with respect to total variation and Wasserstein distances.

Extended analysis to regime-switching Markov processes with jumps.

Abstract

In this article, we discuss subgeometric ergodicity of a class of regime-switching diffusion processes. We derive conditions on the drift and diffusion coefficients, and the switching mechanism which result in subgeometric ergodicity of the corresponding semigroup with respect to the total variation distance as well as a class of Wasserstein distances. At the end, subgeometric ergodicity of certain classes of regime-switching Markov processes with jumps is also discussed.