Markov chains on Z +Citation formats

Standard

Markov chains on Z + : analysis of stationary measure via harmonic functions approach. / Denisov, Denis; Korshunov, Dmitry; Wachtel, Vitali.

In: Queueing Systems, 2019.

Research output: Contribution to journalArticle

Harvard

APA

Vancouver

Author

Denisov, Denis ; Korshunov, Dmitry ; Wachtel, Vitali. / Markov chains on Z + : analysis of stationary measure via harmonic functions approach. In: Queueing Systems. 2019.

Bibtex

@article{9c49f016656c477abb2b06fc630f9294,
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’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 = "Exponential change of measure, Harmonic function, Markov chain, Queues, Renewal function, Stationary distribution, Transition kernel",
author = "Denis Denisov and Dmitry Korshunov and Vitali Wachtel",
year = "2019",
doi = "10.1007/s11134-019-09602-5",
language = "English",
journal = "Queueing Systems",
issn = "0001-4346",
publisher = "Springer Nature",

}

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

PY - 2019

Y1 - 2019

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 - Exponential change of measure

KW - Harmonic function

KW - Markov chain

KW - Queues

KW - Renewal function

KW - Stationary distribution

KW - Transition kernel

U2 - 10.1007/s11134-019-09602-5

DO - 10.1007/s11134-019-09602-5

M3 - Article

JO - Queueing Systems

JF - Queueing Systems

SN - 0001-4346

ER -