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| HAL : hal-00503150, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Variable length Markov chains and dynamical sources |
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| Peggy Cénac 1Brigitte Chauvin 2 |
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| (16/07/2010) |
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| Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the ``comb'' and the ``bamboo blossom'', we find a necessary and sufficient condition for the existence and the unicity of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the generating functions of word occurrences. |
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| 1 : | Institut de Mathématiques de Bourgogne (IMB) |
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CNRS : UMR5584 – Université de Bourgogne |
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| 2 : | Laboratoire de Mathématiques de Versailles (LM-Versailles) |
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CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines |
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| 3 : | Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA) |
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CNRS : UMR6140 – Université de Picardie Jules Verne |
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| LMV, UMR 8100;IMB, UMR 5584;LAMFA, UMR 6140 |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Systèmes dynamiques |
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| Variable length Markov chains – Dynamical systems of the interval – Dirichlet series – Occurrences of words – Probabilistic dynamical sources |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00503150, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00503150 | |
| oai:hal.archives-ouvertes.fr:hal-00503150 | |
| Contributeur : Nicolas Pouyanne | |
| Soumis le : Samedi 17 Juillet 2010, 07:54:14 | |
| Dernière modification le : Dimanche 18 Juillet 2010, 12:51:04 | |
