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Exponential ergodicity and convergence for generalized reflected Brownian motion

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  • Wenpin Tang

    (University of California)

Abstract

In this paper, we provide convergence analysis for a class of Brownian queues in tandem by establishing an exponential drift condition. A consequence is uniform exponential ergodicity for these multidimensional diffusions, including the O’Connell–Yor process. A list of open problems is also presented.

Suggested Citation

  • Wenpin Tang, 2019. "Exponential ergodicity and convergence for generalized reflected Brownian motion," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 83-101, June.
    • Handle: RePEc:spr:queues:v:92:y:2019:i:1:d:10.1007_s11134-019-09610-5
    DOI: 10.1007/s11134-019-09610-5
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    References listed on IDEAS

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    1. Budhiraja, Amarjit & Lee, Chihoon, 2007. "Long time asymptotics for constrained diffusions in polyhedral domains," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1014-1036, August.
    2. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    3. J. Dai & J. Harrison, 2012. "Reflecting Brownian motion in three dimensions: a new proof of sufficient conditions for positive recurrence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 135-147, April.
    4. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    5. Robert B. Lund & Richard L. Tweedie, 1996. "Geometric Convergence Rates for Stochastically Ordered Markov Chains," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 182-194, February.
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