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

Aziz Khanchi ()
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Aziz Khanchi: University of Ottawa

Journal of Theoretical Probability, 2012, vol. 25, issue 1, 62-76

Abstract: 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.

Keywords: Markov additive chain; Harmonic function; Green’s function; Invariant measure; Yaglom limit; 60J10; 60K15 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0384-1

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