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Countable non-homogeneous Markov chains: asymptotic behaviour

Published online by Cambridge University Press:  01 July 2016

Harry Cohn
Harry Cohn*
Affiliation:
The Australian National University
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Abstract

The paper deals with asymptotic properties of the transition probabilities of a countable non-homogeneous Markov chain, the main concept used in the proofs being that of the tail σ-field of the chain. A state classification similar to that existing in the homogeneous case is given and a strong ratio limit property is shown to parallel the basic limit theorem for positive homogeneous chains. Some global asymptotic properties for null chains are also derived.

Keywords

NON-HOMOGENEOUS CHAINHOMOGENEOUS CHAINTAIL σ-FIELDATOMIC SETCOMPLETELY NON-ATOMIC SETMARTINGALESTRONG RATIO LIMIT THEOREM
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 3 , September 1977 , pp. 542 - 552
Copyright
Copyright © Applied Probability Trust 1977 

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References

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