%0 Journal Article %1 vandoorn2017asymptotic %A van Doorn, Erik A. %D 2017 %K birth-death-process %T Asymptotic period of an aperiodic Markov chain %U http://arxiv.org/abs/1712.10199 %X We introduce the concept of asymptotic period for an irreducible and aperiodic, discrete-time Markov chain X on a countable state space, and develop the theory leading to its formal definition. The asymptotic period of X equals one - its period - if X is recurrent, but may be larger than one if X is transient; X is asymptotically aperiodic if its asymptotic period equals one. Some sufficient conditions for asymptotic aperiodicity are presented. The asymptotic period of a birth-death process on the nonnegative integers is studied in detail and shown to be equal to 1, 2 or infinity. Criteria for the occurrence of each value in terms of the 1-step transition probabilities are established.

@article{vandoorn2017asymptotic, abstract = {We introduce the concept of asymptotic period for an irreducible and aperiodic, discrete-time Markov chain X on a countable state space, and develop the theory leading to its formal definition. The asymptotic period of X equals one - its period - if X is recurrent, but may be larger than one if X is transient; X is asymptotically aperiodic if its asymptotic period equals one. Some sufficient conditions for asymptotic aperiodicity are presented. The asymptotic period of a birth-death process on the nonnegative integers is studied in detail and shown to be equal to 1, 2 or infinity. Criteria for the occurrence of each value in terms of the 1-step transition probabilities are established.}, added-at = {2018-01-02T16:41:36.000+0100}, author = {van Doorn, Erik A.}, biburl = {https://www.bibsonomy.org/bibtex/29b8f659cec59135df27f856839564579/claired}, description = {Asymptotic period of an aperiodic Markov chain}, interhash = {cb9c16ebdff5672d04879d3ada278270}, intrahash = {9b8f659cec59135df27f856839564579}, keywords = {birth-death-process}, note = {cite arxiv:1712.10199Comment: 19 pages}, timestamp = {2018-01-02T16:41:36.000+0100}, title = {Asymptotic period of an aperiodic Markov chain}, url = {http://arxiv.org/abs/1712.10199}, year = 2017 }