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27823 Asymptotic period of an aperiodic Markov chain and the strong ratio limit property
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van Doorn, E.A. (2017) Asymptotic period of an aperiodic Markov chain and the strong ratio limit property. Memorandum 2059, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850

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Abstract

We introduce the concept of asymptotic period for an irreducible and aperiodic discrete-time Markov chain on a countable state space. If the chain is transient its asymptotic period may be larger than one. We present some sufficient conditions and, in the more restricted setting of birth-death processes, a necessary and sufficient condition for asymptotic aperiodicity. It is subsequently shown that a birth-death process has the strong ratio limit property if a related birth-death process is asymptotically aperiodic. In the general setting a similar statement is not true, but validity of the converse implication is posed as a conjecture.

Item Type:Internal Report (Memorandum)
Research Group:EWI-SOR: Stochastic Operations Research
Uncontrolled Keywords:aperiodicity, birth-death process, harmonic function, invariant measure, invariant vector, period, ratio limit, transient Markov chain, transition probability
ID Code:27823
Deposited On:09 March 2017
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