Feller property of regime-switching jump diffusion processes with hybrid jumps

Abstract.: The transition kernel of an ℝⁿ-valued diffusion or jump diffusion process {X_t} is known to satisfy the Feller property if {X_t} is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X_t} is the solution of an SDE whose coefficients depend on a state-dependent regime-switching process {θ_t}. In this paper it is shown that pathwise uniqueness and the Feller property are satisfied under mild conditions for a regime-switching jump diffusion process {X_t, θ_t} with hybrid jumps, i.e. jumps in {X_t} that occur simultaneously with {θ_t} switching.