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Multidimensional sticky Brownian motions: Heavy traffic limit and rough tail asymptotics

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  • Dai, Hongshuai
  • Zhao, Yiqiang Q.

Abstract

Inspired by the concept of sticky Brownian motion on the half-line, we investigate a time-changed semimartingale reflecting Brownian motion in the orthant, which we refer to as multidimensional sticky Brownian motion. We first show that it can be obtained as a natural diffusion approximation for a certain tandem queue with exceptional arrival rates. Furthermore, we examine the tail dependence structure of the joint stationary distribution. Under some mild conditions, we derive rough tail asymptotics for the joint stationary distribution. Finally, in some special cases, we present the exact tail asymptotics of the joint stationary distribution.

Suggested Citation

  • Dai, Hongshuai & Zhao, Yiqiang Q., 2025. "Multidimensional sticky Brownian motions: Heavy traffic limit and rough tail asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001863
    DOI: 10.1016/j.spa.2025.104743
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    References listed on IDEAS

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    1. Delgado, Rosario, 2007. "A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 188-201, February.
    2. Peter D. Welch, 1964. "On a Generalized M / G /1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service," Operations Research, INFORMS, vol. 12(5), pages 736-752, October.
    3. Dai, J.G. & Miyazawa, Masakiyo & Wu, Jian, 2015. "Decomposable stationary distribution of a multidimensional SRBM," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1799-1820.
    4. Yamada, Keigo, 1994. "Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 135-164, August.
    5. Kei Kobayashi, 2011. "Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 24(3), pages 789-820, September.
    6. Dupuis, Paul & Ramanan, Kavita, 2002. "A time-reversed representation for the tail probabilities of stationary reflected Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 253-287, April.
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