1982•Journal of Applied ProbabilityRequires access

Weak lumpability in finite Markov chains

Atef M. Abdel-moneim, Frederick W. Leysieffer

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.

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Key concepts: Mathematics, Markov chain, Partition (number theory), Balance equation, Markov kernel, Markov chain mixing time, Additive Markov chain, Continuous-time Markov chain