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Given a Markov chain on a countable state space, we present a Lyapunov (sufficient) condition for existence of an invariant probability with a geometric tail.
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References
1
1.Hernández-Lerma, O. & Lasserre, J.B. (1995). Invariant probabilities for Feller Markov chains. Journal of Applied Mathematics and Stochastic Analysis8: 341–345.CrossRefGoogle Scholar
2
2.Lasserre, J.B. (1997). Invariant probabilities for Markov chains on a metric space. Statistics and Probability Letters34: 259–265.CrossRefGoogle Scholar
3
3.Lasserre, J.B. & Tijms, H. (1996). Invariant probabilities with geometric tail. Probability in the Engineering and Informational Sciences10: 213–221.CrossRefGoogle Scholar
4
4.Malyshev, V.A. & Menshikov, M.V. (1981). Ergodicity, continuity and analyticity of countable Markov chains. Transactions of the Moscow Mathematics Society1: 1–48.Google Scholar
5
5.Royden, H.L. (1988). Real analysis. New York: Macmillan.Google Scholar
6
6.Spieksma, F.M. & Tweedie, R.L. (1994). Strengthening ergodicity to geometric ergodicity of Markov chains. Stochastic Models10: 45–75.CrossRefGoogle Scholar
7
7.Takahashi, Y. (1981). Asymptotic exponentiality of the tail of the waiting time distribution in a Ph/Ph/c queue. Advances in Applied Probability13: 619–630.CrossRefGoogle Scholar
8
8.Tijms, H.C. (1994). Stochastic models: An algorithmic approach. Chichester: John Wiley & Sons Ltd.Google Scholar