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

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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 languageEnglish (US)
Pages (from-to)493-497
Number of pages5
JournalProceedings of the American Mathematical Society
Volume89
Issue number3
DOIs
StatePublished - Jan 1 1983

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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