Equivalent Conditions for Irreducibility of Discrete Time Markov Chains

Cuong Le Van () and John Stachurski
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Cuong Le Van: CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain, CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
John Stachurski: CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain

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Abstract: We consider discrete time Markov chains on general state space. It is shown that a certain property referred to here as nondecomposability is equivalent to irreducibility, and that a Markov chain with invariant distribution is irreducible if and only if the invariant distribution is unique and assigns positive probability to all absorbing sets.

Keywords: discrete time Markov chains; invariant distribution; nondecomposability; irreducibility; absorbing set; chaînes de Markov à temps discret; distribution invariante; nondécomposabilité; irréductibilité; ensemble absorbant (search for similar items in EconPapers)
Date: 2004-06
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03331248
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Published in 2004

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