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Lumpability for non-irreducible finite markov chains
Atef M. Abdel-Moneim, Frederick W. Leysieffer
Journal:

Journal of Applied Probability / Volume 21 / Issue 3 / September 1984

Published online by Cambridge University Press:

14 July 2016, pp. 567-574

Print publication:

September 1984
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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.

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Lumpability for non-irreducible finite markov chains