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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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Official URL: http://www.math.utwente.nl/publications/
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.
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