Abstract: Reflected diffusions with jumps occur in many financial as well as queueing network models. There has been much work by Williams and Harrison on Semi-martingale Reflected Brownian Motion (SRBM) (ICM 1998) and the boundary characterization of such processes. However there are few results for reflected diffusions with jumps with non-constant drifts and diffusion coefficients. In the talk I will present 2 new sets of results for diffusions with jumps and oblique reflections at the boundary. The first is a characterization of the boundary behavior in terms of the local time and a result on the support of the distribution on the boundary surfaces. In particular the results generalize some earlier results due to Taylor and Williams (PTRF 1993) and Guillemin and the speaker (Appl. Math. Opt. 1996). In the second part, we exploit the boundary characterization to obtain the necessary and sufficient conditions for the existence of product-form stationary distributions that generalize the Harrison-Williams result for SRBM (Stochastics 1987). I will conclude with some examples for which explicit results can be obtained. Based on joint work with Dr. Fabrice Guillemin (CNET, France) and Francisco Piera (Purdue).

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