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Simulating tail asymptotics of a Markov chain

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  • Khanchi, Aziz
  • Lamothe, Gilles

Abstract

This paper develops a rare event simulation algorithm for a discrete-time Markov chain in the first orthant. The algorithm gives a very good estimate of the stationary distribution along one of the axes and it is shown to be efficient. A key idea is to study an associated time reversed Markov chain that starts at the rare event. We will apply the algorithm to a Markov chain related to a Jackson network with two stations.

Suggested Citation

  • Khanchi, Aziz & Lamothe, Gilles, 2011. "Simulating tail asymptotics of a Markov chain," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1392-1397, September.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1392-1397
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    References listed on IDEAS

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    1. Masakiyo Miyazawa, 2009. "Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 547-575, August.
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