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-switching diffusion processes in an infinite state space, which could be time-inhomogeneous and state-dependent. Then the strong Feller properties of these processes are investigated by using the theory of parabolic differential equations and dimensional-free Harnack inequalities.