FORWARD EQUATIONS FOR REFLECTED DIFFUSIONS WITH JUMPS

In this paper we obtain the forward equations associated with the evol ution of the density, if it exists, of reflected diffusions on the pos itive orthant with jumps which form a marked point process whose rando m jump measure possesses a stochastic intensity. These results general ize the so-called generalized Dynkin equations for piecewise determini stic jump processes due to Davis. We then consider the stationary case where the existence of a stochastic intensity is not needed. The tech niques are based on local times and the use of random jump measures. W e discuss the application of these results to problems arising in queu ing and storage processes as well as stationary distributions of diffu sions with delayed and jump reflections at the origin.