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Asymptotics of Markov Additive Chains on a Half-Plane: A Ratio Limit Theorem

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  • Aziz Khanchi

    (University of Ottawa)

Abstract

Consider a Markov additive chain (V,Z) with a negative horizontal drift on a half-plane. We provide the limiting distribution of Z when V passes a threshold for the first time, as V tends to infinity. Our contribution is to allow the Markovian part of an associated twisted Markov chain to be null recurrent or transient. The positive recurrent case was treated by Kesten [Ann. Probab. 2 (1974), 355–386]. Moreover, a ratio limit will be established for a transition kernel with unbounded jumps.

Suggested Citation

  • Aziz Khanchi, 2012. "Asymptotics of Markov Additive Chains on a Half-Plane: A Ratio Limit Theorem," Journal of Theoretical Probability, Springer, vol. 25(1), pages 62-76, March.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-011-0384-1
    DOI: 10.1007/s10959-011-0384-1
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    References listed on IDEAS

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    1. Högnäs, Göran, 1997. "On the quasi-stationary distribution of a stochastic Ricker model," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 243-263, October.
    2. 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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