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XXIV.—Conditions for the Ergodicity of Non-homogeneous Finite Markov Chains*

Published online by Cambridge University Press:  14 February 2012

J. L. Mott
J. L. Mott
Affiliation:
University of Edinburgh
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Synopsis

In this note we study the asymptotic behaviour of a product of matrices where Pj is a matrix of transition probabilities in a non-homogeneous finite Markov chain. We give conditions that (i) the rows of P(n) tend to identity and that (ii) P(n) tends to a limit matrix with identical rows.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 64 , Issue 4 , 1957 , pp. 369 - 380
Copyright
Copyright © Royal Society of Edinburgh 1957

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References

Hajnal, J., 1956. “The ergodic properties of non-homogeneous finite Markov chains”, Proc. Camb. Phil. Soc., 52, 67–77.CrossRefGoogle Scholar