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  • Harmonic_Cramer_Q

    Rights statement: The final publication is available at Springer via https://doi.org/10.1007/s11134-019-09602-5

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Markov chains on Z +: analysis of stationary measure via harmonic functions approach

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<mark>Journal publication date</mark>1/04/2019
<mark>Journal</mark>Queueing Systems
Issue number3-4
Volume91
Number of pages31
Pages (from-to)265–295
Publication statusPublished
Early online date19/02/19
Original languageEnglish

Abstract

We suggest a method for constructing a positive harmonic function for a wide class of transition kernels on Z + . We also find natural conditions under which this harmonic function has a positive finite limit at infinity. Further, we apply our results on harmonic functions to asymptotically homogeneous Markov chains on Z + with asymptotically negative drift which arise in various queueing models. More precisely, assuming that the Markov chain satisfies Cramér’s condition, we study the tail asymptotics of its stationary distribution. In particular, we clarify the impact of the rate of convergence of chain jumps towards the limiting distribution.

Bibliographic note

The final publication is available at Springer via https://doi.org/10.1007/s11134-019-09602-5