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.