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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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https://hal.inria.fr/inria-00073889
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Submitted on : Wednesday, May 24, 2006 - 1:59:57 PM
Last modification on : Friday, February 4, 2022 - 3:25:07 AM
Long-term archiving on: : Monday, April 5, 2010 - 12:01:03 AM

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  • HAL Id : inria-00073889, version 1

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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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