An invariance principle for semimartingale reflecting Brownian motions in an orthant |
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Authors: | Williams RJ |
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Institution: | (1) Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA |
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Abstract: | Semimartingale reflecting Brownian motions in an orthant (SRBMs) are of interest in applied probability because of their role
as heavy traffic approximations for open queueing networks. It is shown in this paper that a process which satisfies the definition
of an SRBM, except that small random perturbations in the defining conditions are allowed, is close in distribution to an
SRBM. This perturbation result is called an invariance principle by analogy with the invariance principle of Stroock and Varadhan
for diffusions with boundary conditions. A crucial ingredient in the proof of this result is an oscillation inequality for
solutions of a perturbed Skorokhod problem. In a subsequent paper, the invariance principle is used to give general conditions
under which a heavy traffic limit theorem holds for open multiclass queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | semimartingale reflecting Brownian motion diffusions invariance principle Skorokhod problem oscillation inequality open multiclass queueing networks |
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