Periodic solutions of hybrid jump diffusion processes

TL;DR

This paper studies the existence and uniqueness of periodic solutions in hybrid jump diffusion processes with regime switching, establishing foundational properties like well-posedness, strong Feller property, and irreducibility.

Contribution

It introduces new results on periodic solutions for hybrid jump diffusions, including well-posedness and semigroup properties, with concrete examples demonstrating applicability.

Findings

Proved well-posedness of hybrid jump diffusion SDEs

Established strong Feller property and irreducibility

Proved existence and uniqueness of periodic solutions

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.