Probabilistic bisimulations of switching and resetting diffusions

This contribution presents sufficient conditions for the existence of probabilistic bisimulations between two diffusion processes that are additionally endowed with switching and resetting behaviors. A probabilistic bisimulation between two stochastic processes is defined by means of a bisimulation function, which induces an approximation metric over the distance between the two processes. The validity of the proposed sufficient conditions results in the explicit characterization of one such bisimulation function. The conditions depend on contractivity properties of the two stochastic processes.