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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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Markov chains on Z +: analysis of stationary measure via harmonic functions approach. / Denisov, Denis; Korshunov, Dmitry; Wachtel, Vitali.
In: Queueing Systems, Vol. 91, No. 3-4, 01.04.2019, p. 265–295.

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Denisov D, Korshunov D, Wachtel V. Markov chains on Z +: analysis of stationary measure via harmonic functions approach. Queueing Systems. 2019 Apr 1;91(3-4):265–295. Epub 2019 Feb 19. doi: 10.1007/s11134-019-09602-5

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Denisov, Denis ; Korshunov, Dmitry ; Wachtel, Vitali. / Markov chains on Z + : analysis of stationary measure via harmonic functions approach. In: Queueing Systems. 2019 ; Vol. 91, No. 3-4. pp. 265–295.

Bibtex

@article{853ffa6f72c24b64894b397a59aa288b,
title = "Markov chains on Z +: analysis of stationary measure via harmonic functions approach",
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 Cram{\'e}r{\textquoteright}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. ",
keywords = "Transition kernel, Harmonic function, Markov chain, Stationary distribution, Renewal function, Exponential change of measure, Queues",
author = "Denis Denisov and Dmitry Korshunov and Vitali Wachtel",
note = "The final publication is available at Springer via https://doi.org/10.1007/s11134-019-09602-5",
year = "2019",
month = apr,
day = "1",
doi = "10.1007/s11134-019-09602-5",
language = "English",
volume = "91",
pages = "265–295",
journal = "Queueing Systems",
issn = "0257-0130",
publisher = "Springer Netherlands",
number = "3-4",

}

RIS

TY - JOUR

T1 - Markov chains on Z +

T2 - analysis of stationary measure via harmonic functions approach

AU - Denisov, Denis

AU - Korshunov, Dmitry

AU - Wachtel, Vitali

N1 - The final publication is available at Springer via https://doi.org/10.1007/s11134-019-09602-5

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - Transition kernel

KW - Harmonic function

KW - Markov chain

KW - Stationary distribution

KW - Renewal function

KW - Exponential change of measure

KW - Queues

U2 - 10.1007/s11134-019-09602-5

DO - 10.1007/s11134-019-09602-5

M3 - Journal article

VL - 91

SP - 265

EP - 295

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

IS - 3-4

ER -