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Reflecting Brownian motion in three dimensions: a new proof of sufficient conditions for positive recurrence

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Abstract

Let Z = {Z(t), t ≥ 0} be a semimartingale reflecting Brownian motion that lives in the three-dimensional non-negative orthant. A 2002 paper by El Kharroubi, Ben Tahar and Yaacoubi gave sufficient conditions for positive recurrence of Z. Recently Bramson, Dai and Harrison have shown that those conditions are also necessary for positive recurrence. In this paper we provide an alternative proof of sufficiency, the salient feature of which is its use of a linear Lyapunov function.

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Authors and Affiliations

  1. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    J. G. Dai

  2. Graduate School of Business, Stanford University, Stanford, CA, 94305-5015, USA

    J. M. Harrison

Authors
  1. J. G. Dai
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  2. J. M. Harrison
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Corresponding author

Correspondence to J. G. Dai.

Additional information

This research was supported in part by NSF grants CMMI-0727400, CMMI-0825840, and CMMI-1030589 and by an IBM Faculty Award.

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Dai, J.G., Harrison, J.M. Reflecting Brownian motion in three dimensions: a new proof of sufficient conditions for positive recurrence. Math Meth Oper Res 75, 135–147 (2012). https://doi.org/10.1007/s00186-010-0304-7

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  • DOI: https://doi.org/10.1007/s00186-010-0304-7

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