Periodic solutions of hybrid jump diffusion processes

Abstract

In this paper, we investigate periodic solutions of regime-switching jump diffusions. We first show the well-posedness of solutions to the SDEs corresponding to the hybrid system. Then, we derive the strong Feller property and irreducibility of the associated time-inhomogeneous semigroups. Finally, we establish the existence and uniqueness of periodic solutions. Concrete examples are presented to illustrate the results.

This paper is a continuation paper of arXiv:1905.04843. arXiv:1905.04843 discusses periodic solutions of stochastic differential equations driven by Levy noises. The present paper uses some results and techniques of arXiv:1905.04843 to investigate periodic solutions of regime-switching jump diffusions