Strong solutions and strong Feller properties for regime-switching diffusion processes in an infinite state space

摘要

We establish the existence and pathwise uniqueness of regime-switchingdiffusion processes in an infinite state space, which could betime-inhomogeneous and state-dependent. Then the strong Feller properties ofthese processes are investigated by using the theory of parabolic differentialequations and dimensional-free Harnack inequalities.