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Lumpability for non-irreducible finite markov chains

Published online by Cambridge University Press:  14 July 2016

Atef M. Abdel-Moneim  and
Frederick W. Leysieffer
Atef M. Abdel-Moneim*
Affiliation:
Cairo University
Frederick W. Leysieffer*
Affiliation:
The Florida State University
*
∗Postal address: West Heliopolis Post Office, 8 Ahmed Abdel Salam Zaki Street, Apartment #5, Cairo, Egypt.
∗∗Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, U.S.A.
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Abstract

Conditions under which a function of a finite, discrete-time Markov chain, X(t), is again Markov are given, when X(t) is not irreducible. These conditions are given in terms of an interrelationship between two partitions of the state space of X(t), the partition induced by the minimal essential classes of X(t) and the partition with respect to which lumping is to be considered.

Keywords

FUNCTIONS OF MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 567 - 574
Copyright
Copyright © Applied Probability Trust 1984 

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References

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[5] Leysieffer, F. W. (1967) Functions of finite Markov chains. Ann. Math. Statist. 38, 206–212.Google Scholar