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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The tail $ \sigma $-field of a finitely additive Markov chain starting from a recurrent state


Author: S. Ramakrishnan
Journal: Proc. Amer. Math. Soc. 89 (1983), 493-497
MSC: Primary 60F20; Secondary 60J10
MathSciNet review: 715873
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0715873-2
PII: S 0002-9939(1983)0715873-2
Keywords: Tail $ \sigma $-field, finitely additive probability, Markov chain, recurrent state
Article copyright: © Copyright 1983 American Mathematical Society