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On the stability of the linear Skorohod problem in an orthant

Author

Listed:
  • Ahmed El Kharroubi
  • Abdelghani Ben Tahar
  • Abdelhak Yaacoubi

Abstract

Dupuis and Williams proved that a sufficient condition for the positive recurrence for a semimartingale reflecting Brownian motion in an orthant (SRBM) with data (θ, R, S, Δ), is that the corresponding Linear Skorohod Problem LSP (θ) is stable. In this paper we use the linear complementary problem to give necessary conditions, on θ∈ℝ n and matrix R, under which the linear Skorohod problem LSP (θ) is stable. In the three dimensional case we characterize the vectors θ∈ℝ 3 such that the LSP (θ) is stable. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Ahmed El Kharroubi & Abdelghani Ben Tahar & Abdelhak Yaacoubi, 2002. "On the stability of the linear Skorohod problem in an orthant," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 243-258, November.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:2:p:243-258
    DOI: 10.1007/s001860200210
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    Cited by:

    1. 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.

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