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- Title
Markov chains on Z+: analysis of stationary measure via harmonic functions approach.
- Authors
Denisov, Denis; Korshunov, Dmitry; Wachtel, Vitali
- 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.
- Subjects
MARKOV processes; HARMONIC functions; INFINITY (Mathematics)
- Publication
Queueing Systems, 2019, Vol 91, Issue 3/4, p265
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-019-09602-5