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.
Regime-switching diffusion processes: strong solutions and strong Feller property
Remarks on the post of Röckner and Zhao about strong solutions of stochastic equations with critical singularities at arXiv:2103.05803v4
On strong solutions of Itô's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$
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