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Reflected Brownian motion with drift in a wedge

Author

Listed:
  • Peter Lakner

    (New York University)

  • Ziran Liu

    (New York University)

  • Josh Reed

    (New York University)

Abstract

We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provides necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem with drift, and show that its solution possesses the Markov and Feller properties. Next, we study a version of the problem with absorption at the vertex of the wedge. In this case, we provide a condition for existence and uniqueness of a solution to the problem and some results on the probability of the vertex being reached.

Suggested Citation

  • Peter Lakner & Ziran Liu & Josh Reed, 2023. "Reflected Brownian motion with drift in a wedge," Queueing Systems: Theory and Applications, Springer, vol. 105(3), pages 233-270, December.
    • Handle: RePEc:spr:queues:v:105:y:2023:i:3:d:10.1007_s11134-023-09893-9
    DOI: 10.1007/s11134-023-09893-9
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    References listed on IDEAS

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    1. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    2. Sandro Franceschi & Kilian Raschel, 2022. "A dual skew symmetry for transient reflected Brownian motion in an orthant," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 123-141, October.
    3. William P. Peterson, 1991. "A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 90-118, February.
    Full references (including those not matched with items on IDEAS)

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