Asymptotic period of an aperiodic Markov chain and the strong ratio limit property

Erik A. van Doorn

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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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages25
Publication statusPublished - Mar 2017

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
ISSN (Print)1874-4850


  • ratio limit
  • invariant vector
  • Invariant Measure
  • transition probability
  • transient Markov chain
  • period
  • IR-104041
  • aperiodicity
  • Birth-death process
  • MSC-60J10
  • EWI-27823
  • MSC-60J80
  • harmonic function

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