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

摘要

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