Rights statement: The final publication is available at Springer via https://doi.org/10.1007/s11134-019-09602-5
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Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -