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Reports (Research Report) Year : 1996

Weak Lumpability of Finite Markov Chains and Positive Invariance of Cones

James Ledoux

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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Dates and versions

inria-00073889 , version 1 (24-05-2006)

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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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