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A note on Foster-Lyapunov drift condition for recurrence of Markov chains on general state spaces. (English) Zbl 1428.60101

Summary: In this paper, we prove that the Foster-Lyapunov drift condition is necessary and sufficient for recurrence of a Markov chain on a general state space. And then an answer in the affirmative for the question presented in the monograph of S. P. Meyn and R. L. Tweedie [Markov chains and stochastic stability. Berlin: Springer-Verlag (1993; Zbl 0925.60001), p. 175] is obtained.

MSC:

60J05 Discrete-time Markov processes on general state spaces

Citations:

Zbl 0925.60001
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References:

[1] Foster, FG, On the stochastic matrices associated with certain queueing processes, Ann. Math. Stat., 24, 335-360, (1953) · Zbl 0051.10601 · doi:10.1214/aoms/1177728976
[2] Mertens, JF; Samuel-Cahn, E.; Zamir, S., Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities, J. Appl. Probab., 15, 848-851, (1978) · Zbl 0398.60068 · doi:10.2307/3213440
[3] Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Springer, Berlin (1993) · doi:10.1007/978-1-4471-3267-7
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