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Weak lumpability in 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:
The Florida State University
Frederick W. Leysieffer*
Affiliation:
The Florida State University
*
∗Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, U.S.A.
∗Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, U.S.A.
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Abstract

Criteria are given to determine whether a given finite Markov chain can be lumped weakly with respect to a given partition of its state space. These conditions are given in terms of solution classes of systems of linear equations associated with the transition probability matrix of the Markov chain and the given partition.

Keywords

LUMPABILITYMARKOV CHAINSWEAK LUMPABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 685 - 691
Copyright
Copyright © Applied Probability Trust 1982 

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References

[1] Burke, C. J. and Rosenblatt, M. (1958) A Markovian function of a finite Markov chain. Ann. Math. Statist. 29, 1112–1122.Google Scholar
[2] Hachigian, J. and Rosenblatt, M. (1963) Collapsed Markov chains and the Chapman–Kolmogorov equation. Ann. Math. Statist. 34, 233–237.Google Scholar
[3] Kemeny, J. G. and Snell, J. L. (1978) Finite Markov Chains, 2nd edn. Springer-Verlag, New York.Google Scholar