  A comparison theorem for state-dependent regime-switching diffusion processes
is established, which enables us to control pathwisely the evolution of the
state-dependent switching component simply by Markov chains. Moreover, a sharp
estimate on the stability of Markovian regime-switching processes under the
perturbation of transition rate matrices is provided. Our approach is based on
the elaborate constructions of switching processes in the spirit of Skorokhod's
representation theorem varying according to the problem being dealt with. In
particular, this method can cope with the switching processes in an infinite
state space and not necessarily being of birth-death type. As an application,
some known results on ergodicity and stability of state-dependent
regime-switching processes can be improved.
