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Reflected Brownian motion in the quarter plane: An equivalence based on time reversal

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  • Harrison, J. Michael

Abstract

We consider a semimartingale reflected Brownian motion (SRBM) Z whose state space is the non-negative quarter plane; the apparently more general case of SRBM in a convex wedge can be transformed to the quarter plane by a simple change of variable. The data of the stochastic process Z are a drift vector μ, a covariance matrix Σ, and a 2 × 2 reflection matrix R whose columns are the directions of reflection on the two axes. We consider only the case where R has non-positive off-diagonal elements, that is, the direction of reflection is either normal or toward the origin from each axis.

Suggested Citation

  • Harrison, J. Michael, 2022. "Reflected Brownian motion in the quarter plane: An equivalence based on time reversal," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1189-1203.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:1189-1203
    DOI: 10.1016/j.spa.2021.12.003
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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. Ernst, Philip A. & Franceschi, Sandro & Huang, Dongzhou, 2021. "Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 634-670.
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    Cited by:

    1. 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.

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