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Ergodic theorems for sequences of infinite stochastic matrices

Published online by Cambridge University Press:  24 October 2008

A. Paz  and
M. Reichaw
A. Paz
Affiliation:
Technion, I.I.T., Haifa, Israel
M. Reichaw
Affiliation:
Technion, I.I.T., Haifa, Israel
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Extract

In the theory of finite state, discrete time, non-homogeneous Markov chains, different notions of ergodicity have been introduced in the literature. These notions are concerned with the long-run behaviour of chains and with their tendency to get some stability properties after a sufficiently long period of time. The aim of this paper is the study of non-homogeneous Markov chains with a denumerable number of states. It will be shown that some theorems which are valid in the finite case are also valid for chains with a denumerable number of states as well. Moreover, a new notion of stability is introduced and it is shown to be satisfied for some chains. Although the paper is self-contained some familiarity with the theory of finite state non-homogeneous Markov chains is desired. Without any attempt of completeness we list for the interested reader the papers: (1–3, 8, 9).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 777 - 784
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

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