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| HAL : hal-00617189, version 2 |
| arXiv : 1108.5292 |
| Fiche détaillée |  Récupérer au format |
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| ALEA : Latin American Journal of Probability and Mathematical Statistics 9 (2012) 141-163 |
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| Versions disponibles : | v1 (26-08-2011) | v2 (26-01-2012) |
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| The almost sure invariance principle for unbounded functions of expanding maps |
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| Jerome Dedecker 1Sébastien Gouëzel 2 |
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| (2012) |
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| We consider two classes of piecewise expanding maps $T$ of $[0,1]$: a class of uniformly expanding maps for which the Perron-Frobenius operator has a spectral gap in the space of bounded variation functions, and a class of expanding maps with a neutral fixed point at zero. In both cases, we give a large class of unbounded functions $f$ for which the partial sums of $f\circ T^i$ satisfy an almost sure invariance principle. This class contains piecewise monotonic functions (with a finite number of branches) such that: - For uniformly expanding maps, they are square integrable with respect to the absolutely continuous invariant probability measure. - For maps having a neutral fixed point at zero, they satisfy an (optimal) tail condition with respect to the absolutely continuous invariant probability measure. |
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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 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
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| 3 : | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) |
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Université Paris Est Marne-la-Vallée – Université Paris XII - Paris Est Créteil Val-de-Marne – CNRS : UMR8050 – Fédération de Recherche Bézout |
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| Théorie ergodique |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Systèmes dynamiques |
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| Expanding maps – intermittency – strong invariance principle |
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| hal-00617189, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00617189 | |
| oai:hal.archives-ouvertes.fr:hal-00617189 | |
| Contributeur : Sebastien Gouezel | |
| Soumis le : Mercredi 25 Janvier 2012, 16:23:34 | |
| Dernière modification le : Mercredi 9 Mai 2012, 11:18:56 | |
