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

S. Ramakrishnan

doi:10.1090/S0002-9939-1983-0715873-2

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

S. Ramakrishnan

Mathematics

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

1 Scopus citations

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	https://doi.org/10.1090/S0002-9939-1983-0715873-2
State	Published - Nov 1983

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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

Abstract

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