Feller property of regime-switching jump diffusion processes with hybrid jumps (Q6571709)

It is known that the transition kernel of a \(d\)-dimensional diffusion or jump-diffusion process\((X_t)_t\) satisfies the Feller property if it is the solution of an SDE (stochastic differential equation) whose coefficients are Lipschitz continuous. `Feller' is meant here in the sense, that continuous functions are mapped on continuous functions and not in the \(C_0\)- or \(C_b\)-sense. `This Lipschitz route to Feller falls short if \((X_t)_t\) is the solution of an SDE whose coefficients depend on a state-dependent regime-switching process \((\theta_t)_t\). 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 \((\theta_t)_t\) with hybrid jumps, i.e., jumps in \((X_t)_t\) that occur simultaneously with \((\theta_t)_t\) switching.' \N\NSome of the citations are vague: three textbooks are mentioned as sources for a result, not telling the reader where to find the results in the books. On other occasions nice overviews on existing results are given, e.g., in Table 1.