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On weak lumpability in Markov chains

Published online by Cambridge University Press:  14 July 2016

Gerardo Rubino  and
Gerardo Rubino
Gerardo Rubino*
Affiliation:
IRISA
Gerardo Rubino*
Affiliation:
IRISA
*
∗Postal address for both authors: IRISA Campus de Beaulieu, 35042 Rennes Cedex, France.
∗Postal address for both authors: IRISA Campus de Beaulieu, 35042 Rennes Cedex, France.
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Abstract

We analyse the conditions under which the aggregated process constructed from an homogeneous Markov chain over a given partition of the state space is also Markov homogeneous. The past work on the subject is revised and new properties are obtained.

Keywords

AGGREGATIONLUMPABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 446 - 457
Copyright
Copyright © Applied Probability Trust 1989 

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References

Abdel-Moneim, A. M. and Leysieffer, F. W. (1982) Weak lumpability in finite Markov chains. J. Appl. Prob. 19, 685–691.Google Scholar
Kemeny, J. G. and Snell, J. L. (1976) Finite Markov Chains. Springer-Verlag, New York.Google Scholar