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

TL;DR

This paper proves the existence, uniqueness, and strong Feller properties of regime-switching diffusion processes in infinite state spaces, using advanced PDE techniques and Harnack inequalities.

Contribution

It introduces new results on the existence, uniqueness, and regularity of regime-switching diffusions in infinite, possibly time-inhomogeneous, state spaces.

Findings

Existence and pathwise uniqueness of the processes.

Strong Feller property established using PDE and Harnack inequalities.

Applicable to time-inhomogeneous, state-dependent regimes.

Abstract

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.