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| HAL : hal-00654259, version 3 |
| arXiv : 1112.5070 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (21-12-2011) | v2 (03-01-2012) | v3 (03-10-2012) |
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| Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws |
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| Ivan Nourdin 1Jan Rosinski 2 |
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| (21/12/2011) |
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| We characterize the asymptotic independence between blocks consisting of multiple Wiener-Itô integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension, and other related results on the multivariate convergence of multiple Wiener-Itô integrals, that involve Gaussian and non Gaussian limits. We give applications to the study of the asymptotic behavior of functions of short and long range dependent stationary Gaussian time series and establish the asymptotic independence for discrete non-Gaussian chaoses |
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| 1 : | Institut Élie Cartan Nancy (IECN) |
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CNRS : UMR7502 – Université de Lorraine |
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| 2 : | Department of Mathematics [Tennessee] |
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University of Tennessee |
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| Probabilités et statistiques |
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| Domaine | : | Mathématiques/Probabilités |
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| Multiple Wiener-Itô integral – Multiplication formula – Limit theorems |
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| hal-00654259, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00654259 | |
| oai:hal.archives-ouvertes.fr:hal-00654259 | |
| Contributeur : Ivan Nourdin | |
| Soumis le : Mardi 2 Octobre 2012, 16:18:34 | |
| Dernière modification le : Vendredi 5 Avril 2013, 15:54:36 | |
