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On product-form stationary distributions for reflected diffusions with jumps in the positive orthant

Published online by Cambridge University Press:  01 July 2016

Francisco J. Piera*
Affiliation:
Purdue University
Ravi R. Mazumdar*
Affiliation:
University of Waterloo and Purdue University
Fabrice M. Guillemin*
Affiliation:
France Télécom
*
Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA. Email address: [email protected]
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada. Email address: [email protected]
∗∗∗ Postal address: France Télécom R&D, 2 Avenue Pierre Marzin, 22300 Lannion, France. Email address: [email protected]
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Abstract

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In this paper, we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R+n that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusions with oblique boundary reflections and jumps. To do so, we exploit a recent characterization of the boundary properties of such reflected processes. In particular, we show that the conditions generalize those for semimartingale reflecting Brownian motions and reflected Lévy processes. We provide explicit results for some models of interest.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2005 

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