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The ergodic properties of non-homogeneous finite Markov chains

Published online by Cambridge University Press:  24 October 2008

J. Hajnal  and
M. S. Bartlett
J. Hajnal
Affiliation:
Department of Social and Preventive MedicineUniversity of Manchester
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Abstract

The paper deals with the behaviour of finite non-homogeneous Markov chains having regular transition matrices. Two types of ergodic behaviour are distinguished, and sufficient conditions are given for each type. Chains with commutative transition matrices are specially investigated. By means of expansions in terms of the characteristic roots several types of behaviour of chains which are not ergodic are studied.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 67 - 77
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

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