Periodic solutions of hybrid jump diffusion processes

Abstract

We investigate periodic solutions of regime-switching jump diffusions. We first show the well-posedness of solutions to stochastic differential equations 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.

Keywords

Hybrid system / regime-switching jump diffusion / periodic solution / strong Feller property / irreducibility

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