# On Feller and Strong Feller Properties and Exponential Ergodicity of Regime-Switching Jump Diffusion Processes with Countable Regimes

## TL;DR

This paper investigates regime-switching jump diffusion processes with countably infinite regimes, establishing their existence, Feller properties, and exponential ergodicity using coupling and Radon-Nikodym methods.

## Contribution

It introduces a novel approach to analyze processes with infinitely many regimes, proving key properties and ergodicity for this complex class.

## Key findings

- Existence and uniqueness of the process established.
- Feller and strong Feller properties proven.
- Exponential ergodicity demonstrated.

## Abstract

This work focuses on a class of regime-switching jump diffusion processes, in which the switching component has countably infinite many states or regimes. The existence and uniqueness of the underlying process are obtained by an interlacing procedure. Then the Feller and strong Feller properties of such processes are derived by the coupling method and an appropriate Radon-Nikodym derivative. Finally the paper studies exponential ergodicity of regime-switching jump-diffusion processes.