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

The transition kernel of an ℝn-valued diffusion or jump diffusion process Xt is known to satisfy the Feller property if Xt is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if Xt is the solution of an SDE whose coefficients depend on a state-dependent regime-switching process θt. 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 Xt, θt with hybrid jumps, i. e. jumps in Xt that occur simultaneously with θt switching.