Forward equations for reflected diffusions with jumps |
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Authors: | R R Mazumdar F M Guillemin |
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Institution: | (1) INRS-Télécommunications, Université du Quebec, 16 Place du Commerce Ile des Soeurs, H3E 1H6 Quebec, Canada;(2) Centre National d'Etudes des Télécommunications Lannion-A, Route de Trégastel, 22300 Lannion, France |
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Abstract: | In this paper we obtain the forward equations associated with the evolution of the density, if it exists, of reflected diffusions on the positive orthant with jumps which form a marked point process whose random jump measure possesses a stochastic intensity. These results generalize the so-called generalized Dynkin equations for piecewise deterministic jump processes due to Davis. We then consider the stationary case where the existence of a stochastic intensity is not needed. The techniques are based on local times and the use of random jump measures. We discuss the application of these results to problems arising in queuing and storage processes as well as stationary distributions of diffusions with delayed and jump reflections at the origin.This research was supported in part by the Quebec-France Cooperative Research Program and by the Natural Sciences and Engineering Research Council of Canada under Grant OGP 0042024. |
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Keywords: | Diffusions Reflections Semimartingales Random jump measures Stochastic intensity Local time Forward equations Palm probabilities |
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