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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