### Abstract

For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.

Original language | English (US) |
---|---|

Pages (from-to) | 493-497 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 89 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1983 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**The tail σ-field of a finitely additive Markov chain starting from a recurrent state.** / Ramakrishnan, Subramanian.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The tail σ-field of a finitely additive Markov chain starting from a recurrent state

AU - Ramakrishnan, Subramanian

PY - 1983/1/1

Y1 - 1983/1/1

N2 - For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.

AB - For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.

UR - http://www.scopus.com/inward/record.url?scp=84966198413&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966198413&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1983-0715873-2

DO - 10.1090/S0002-9939-1983-0715873-2

M3 - Article

AN - SCOPUS:84966198413

VL - 89

SP - 493

EP - 497

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -