Weak Lumpability of Finite Markov Chains and Positive Invariance of Cones

James Ledoux 1
1 MODEL - Modeling Random Systems
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We consider weak lumpability of general finite homogeneous Markov chains evolving in discrete time, that is when a lumped Markov chain with respect to a partition of the initial state space is also a homogeneous Markov chain. We show that weak lumpability is equivalent to the existence of a decomposable polyhedral cone which is positively invariant by the transition probability matrix of the original chain. It allows us, in a unified way, to derive new results on lumpability of reducible Markov chains and to obtain spectral properties associated with lumpability.
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Rapport
[Research Report] RR-2801, INRIA. 1996
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Soumis le : mercredi 24 mai 2006 - 13:59:57
Dernière modification le : jeudi 11 janvier 2018 - 06:20:09
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James Ledoux. Weak Lumpability of Finite Markov Chains and Positive Invariance of Cones. [Research Report] RR-2801, INRIA. 1996. 〈inria-00073889〉

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