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Activity Number:
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480
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Type:
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Contributed
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Date/Time:
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Wednesday, August 9, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #306088 |
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Title:
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Long Time Asymptotics for Constrained Diffusions in Polyhedral Domains
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Author(s):
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Chihoon Lee*+ and Amarjit Budhiraja
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Companies:
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The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
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Address:
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210 Smith Building, CB 3260, Chapel Hill, NC, 27599,
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Keywords:
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semi-Martingale reflecting Brownian motion ; constrained diffusions ; geometric ergodicity
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Abstract:
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We study long time asymptotic properties of constrained diffusions that arise in the heavy traffic analysis of multiclass queueing networks. We first consider the classical diffusion model with constant coefficients namely a semimartingale reflecting Brownian motion (SRBM), in a d-dimensional positive orthant. Under a natural condition on stability of a related deterministic dynamical system Dupuis and Williams (1994) showed that an SRBM is ergodic. We strengthen this result by establishing geometric ergodicity for the process. As consequences of geometric ergodicity we obtain finiteness of the moment generating function of the invariant measure in a neighborhood of zero, uniform time estimates on moments of the process, and functional central limit results. Similar long time properties are obtained for a broad family of constrained diffusion models with state dependent coefficients.
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