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 | References | Similar Articles | Additional Information

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

Keywords:
Finitely additive probabilities,
strategy,
Markov strategy,
Markov chain,
stationary transition,
stationary initial distribution

Article copyright:
© Copyright 1981
American Mathematical Society