Explicit criteria for recurrence of Markovian regime-switching diffusion processes under arbitrary switching rates

Abstract

The recurrent property of diffusion processes with regime-switching is quite complicated, which could be transient even when it is recurrent at every fixed environment. This work provides explicit criteria in terms of the coefficients of diffusion processes such that the studied processes are recurrent or transient under arbitrary switching rates. The obtained criteria are in the integral form, which are particularly effective for the regime-switching processes with coefficients vibrating periodically. Examples are constructed to illustrate the applications of these criteria.