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Geometrical aspects of the theory of non-homogeneous Markov chains

Published online by Cambridge University Press:  24 October 2008

J. F. C. Kingman
J. F. C. Kingman
Affiliation:
Mathematical Institute, University of Oxford
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Abstract

A geometrical representation of the transition matrices of a non-homogeneous chain with N states, in terms of certain convex subsets of , is used to describe aspects of the chain. For example, an important theorem of Cohn on the structure of the tail σ-field is a simple corollary. The embedding problem is shown to be entirely geometrical in character. The representation extends to Markov processes on quite general state spaces, and the tail is then represented by the projective limit of these convex sets.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 1 , January 1975 , pp. 171 - 183
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

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