Stochastic hybrid system with non-homogeneous jumps

A study of a class of stochastic hybrid dynamic processes is investigated. The hybrid dynamic process is composed of both continuous and discrete time states. In this work we assume that its continuous time state is driven by the Brownian motion process, while the transitions of its discrete time state are governed by either a non-homogeneous Poisson process or by hitting the boundaries. Under this formulation we develop an infinitesimal generator of the stochastic hybrid dynamic process. Moreover we obtain results concerning the quantitative properties of the solution process. A few illustrative examples are presented.