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| HAL : hal-00692546, version 1 |
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| On strong approximation for the empirical process of stationary sequences |
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| Jérôme Dedecker 1Florence Merlevède 2 |
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| (30/04/2012) |
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| We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n−(1+δ) for some positive δ. This shows that our conditions are in some sense optimal. |
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| 1 : | Mathématiques appliquées Paris 5 (MAP5) |
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CNRS : UMR8145 – Université Paris V - Paris Descartes |
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| 2 : | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout |
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| 3 : | Laboratoire de Mathématiques de Versailles (LM-Versailles) |
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CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines |
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| Domaine | : | Mathématiques/Probabilités |
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| Strong approximation – Kiefer process – stationary sequences – intermittent maps – weak dependence |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00692546, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00692546 | |
| oai:hal.archives-ouvertes.fr:hal-00692546 | |
| Contributeur : Florence Merlevède | |
| Soumis le : Lundi 30 Avril 2012, 18:58:33 | |
| Dernière modification le : Mardi 1 Mai 2012, 09:51:18 | |
