Finitely additive markov chains

S. Ramakrishnan

doi:10.1090/S0002-9947-1981-0607119-3

Finitely additive markov chains

S. Ramakrishnan

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

13 Scopus citations

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.

Original language	English (US)
Pages (from-to)	247-272
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	265
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1981-0607119-3
State	Published - May 1981
Externally published	Yes

Keywords

Finitely additive probabilities
Markov chain
Markov strategy
Stationary initial distribution
Stationary transition
Strategy

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1981-0607119-3

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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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AB - 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.

KW - Finitely additive probabilities

KW - Markov chain

KW - Markov strategy

KW - Stationary initial distribution

KW - Stationary transition

KW - Strategy

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Finitely additive markov chains

Abstract

Keywords

ASJC Scopus subject areas

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