941 articles – 1212 references  [version française]
 HAL: hal-00705523, version 1
 Available versions: v1 (2012-06-07) v2 (2013-04-02)
 Generalized eigenfunctions of Markov kernels and application to the convergence rate of discrete random walks
 Denis Guibourg 1, Loïc Hervé 1
 (2012-06-07)
 Let $(X_n)_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. Under a weak drift condition, the size of generalized eigenfunctions of $P$ is estimated, where $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$ associated with $V$. Then combining this result and quasi-compactness arguments enables us to derive upper bounds for the geometric rate of convergence of $(X_n)_{n\in\N}$ to its invariant probability measure in operator norm on $\cB_V$. Applications to discrete Markov random walks are presented.
 1: Institut de Recherche Mathématique de Rennes (IRMAR) 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
 Research team: Théorie ergodiqueStatistique
 Subject : Mathematics/Probability
 Keyword(s): Geometric ergodicity – quasi-compactness – Drift condition – Birth-and -Death Markov chains.
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 hal-00705523, version 1 http://hal.archives-ouvertes.fr/hal-00705523 oai:hal.archives-ouvertes.fr:hal-00705523 From: Loïc Hervé <> Submitted on: Thursday, 7 June 2012 18:03:54 Updated on: Friday, 8 June 2012 08:59:39