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| HAL: hal-00400810, version 1 |
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| Available versions: | v1 (2009-07-02) | v2 (2010-05-31) |
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| Ergodicity of self-attracting motion |
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| Victor Kleptsyn 1Aline Kurtzmann 2 |
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| For the Victor Kleptsyn, Aline Kurtzmann collaboration(s) |
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| (2009-06-25) |
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| The aim of this paper is to study the asymptotic behaviour of a class of self- attracting motions on R^d . Using stochastic approximation methods, these processes have already been studied by Benaïm, Ledoux and Raimond (2002) in a compact setting. We also relate the asymptotic behaviour of the self-attracting Brownian motion to the McKean-Vlasov process that was studied, via the decrease of the free energy, by Carrillo, McCann and Villani (2003). Mixing these methods, we manage to obtain sufficient conditions for the (limit-quotient) ergodicity of the self-attracting diffusion, together with a speed of convergence. |
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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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| 2: | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| Subject | : | Mathematics/Probability |
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| hal-00400810, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00400810 | |
| oai:hal.archives-ouvertes.fr:hal-00400810 | |
| From: Aline Kurtzmann | |
| Submitted on: Thursday, 2 July 2009 09:43:32 | |
| Updated on: Friday, 19 March 2010 09:56:01 | |
