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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Finitely additive Markov chains


Author: S. Ramakrishnan
Journal: Trans. Amer. Math. Soc. 265 (1981), 247-272
MSC: Primary 60J05; Secondary 60G05
MathSciNet review: 607119
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Abstract: In this paper we develop the theory of Markov chains with stationary transition probabilities, where the transition probabilities and the initial distribution are assumed only to be finitely additive. We prove a strong law of large numbers for recurrent chains. The problem of existence and uniqueness of finitely additive stationary initial distributions is studied and the ergodicity of recurrent chains under a stationary initial distribution is proved.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0607119-3
PII: S 0002-9947(1981)0607119-3
Keywords: Finitely additive probabilities, strategy, Markov strategy, Markov chain, stationary transition, stationary initial distribution
Article copyright: © Copyright 1981 American Mathematical Society