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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 61 open journal systems 


Comparison Results for Reflected Jump-diffusions in the Orthant with Variable Reflection Directions and Stability Applications

Francisco J Piera, University of Chile
Ravi R Mazumdar, University of Waterloo


Abstract
We consider reflected jump-diffusions in the orthant $R_+^n$ with time- and state-dependent drift, diffusion and jump-amplitude coefficients. Directions of reflection upon hitting boundary faces are also allow to depend on time and state. Pathwise comparison results for this class of processes are provided, as well as absolute continuity properties for their associated regulator processes responsible of keeping the respective diffusions in the orthant. An important role is played by the boundary property in that regulators do not charge times spent by the reflected diffusion at the intersection of two or more boundary faces. The comparison results are then applied to provide an ergodicity condition for the state-dependent reflection directions case.


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Pages: 1886-1908

Published on: October 30, 2008
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Electronic Journal of Probability. ISSN: 1083-6489