An Invariance Principle for Semimartingale Reflecting Brownian
Motions in Domains with Piecewise Smooth Boundaries
W. Kang and R. J. Williams
Semimartingale Reflecting Brownian Motions (SRBMs) living in the closures of domains
with piecewise smooth boundaries are of interest in applied
probability because of their role as heavy traffic approximations
for some stochastic networks. In this paper, assuming certain
conditions on the domains and directions of reflection, a
perturbation result, or invariance principle, for SRBMs is
proved. This provides sufficient conditions for a process that
satisfies the definition of an SRBM, except for small random
perturbations in the defining conditions, to be close in
distribution to an SRBM. A crucial ingredient in the proof of this
result is an oscillation inequality for solutions of a perturbed
We use the invariance principle to show weak existence of
SRBMs under mild conditions.
We also use the invariance
principle, in conjunction with known uniqueness results
for SRBMs, to give some sufficient
conditions for validating approximations involving (i) SRBMs in convex
polyhedrons with a constant reflection vector field on each face of the
polyhedron, and (ii) SRBMs in bounded domains with
piecewise smooth boundaries
and possibly non-constant reflection vector fields on the boundary
In Annals of Applied Probability, Vol 17 (2007), 741-779.
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For the published article on Project Euclid, click here.
Last updated: May 23, 2006