### Abstract

Original language | English |
---|---|

Pages (from-to) | 759-778 |

Number of pages | 20 |

Journal | Markov processes and related fields |

Volume | 24 |

Issue number | 5 |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- aperiodicity
- birth-death process
- harmonic function
- period
- transient Markov chain
- transition probability

### Cite this

*Markov processes and related fields*,

*24*(5), 759-778.

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*Markov processes and related fields*, vol. 24, no. 5, pp. 759-778.

**Asymptotic period of an aperiodic Markov chain.** / van Doorn, Erik Alexander.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Asymptotic period of an aperiodic Markov chain

AU - van Doorn, Erik Alexander

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - aperiodicity

KW - birth-death process

KW - harmonic function

KW - period

KW - transient Markov chain

KW - transition probability

M3 - Article

VL - 24

SP - 759

EP - 778

JO - Markov processes and related fields

JF - Markov processes and related fields

SN - 1024-2953

IS - 5

ER -