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| HAL : hal-00705523, version 2 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (07-06-2012) | v2 (02-04-2013) |
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| Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks |
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| Denis Guibourg 1Loïc Hervé 1 |
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| (07/06/2012) |
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| Let $\{X_n\}_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. The Markov kernel $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$ associated with $V$. Then the combination of quasi-compactness arguments with precise analysis of eigen-elements of $P$ allows us to estimate the geometric rate of convergence $\rho_V(P)$ of $\{X_n\}_{n\in\N}$ to its invariant probability measure in operator norm on $\cB_V$. A general procedure to compute $\rho_V(P)$ for discrete Markov random walks with identically distributed bounded increments is specified. |
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| 1 : | 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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| Théorie ergodique Statistique |
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| Domaine | : | Mathématiques/Probabilités |
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| Geometric ergodicity – quasi-compactness – Drift condition – Birth-and -Death Markov chains. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00705523, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00705523 | |
| oai:hal.archives-ouvertes.fr:hal-00705523 | |
| Contributeur : Loïc Hervé | |
| Soumis le : Samedi 30 Mars 2013, 12:10:20 | |
| Dernière modification le : Mardi 2 Avril 2013, 14:06:21 | |
