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| HAL: hal-00447075, version 1 |
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| Lecture notes in control and information sciences 341 (2006) 153-160 |
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| Positive invariance of polyhedrons and comparison of Markov reward models with different state spaces |
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| Mourad Ahmane 1James Ledoux 2 |
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| (2006) |
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| In this paper, we discuss the comparison of expected rewards for discrete-time reward Markov chains with different state spaces. Necessary and sufficient conditions for such a comparison are derived. Due to the special nature of the introduced binary relation, a criterion may be formulated in terms of an inclusion of polyhedral sets. Then, algebraic and geometric forms are easily obtained from Haar's Lemma. Our results allow us to discuss some earlier results on the stochastic comparison of functions of Markov chains. |
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| 1: | Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN) |
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CNRS : UMR6597 – PRES Université Nantes Angers Le Mans [UNAM] – École Centrale de Nantes – École Nationale Supérieure des Mines - Nantes – Ecole Polytechnique de l'Université de Nantes |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | École nationale supérieure des Mines de Nantes |
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École Nationale Supérieure des Mines - Nantes – Groupe des Écoles des Mines (GEM) |
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| Subject | : | Mathematics/Probability |
| hal-00447075, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00447075 | |
| oai:hal.archives-ouvertes.fr:hal-00447075 | |
| From: Maryse Collin | |
| Submitted on: Thursday, 14 January 2010 10:58:14 | |
| Updated on: Thursday, 14 January 2010 11:04:17 | |
