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| HAL : hal-00264472, version 1 |
| arXiv : 0803.2441 |
| Fiche détaillée |  Récupérer au format |
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| ON A SZEGO TYPE LIMIT THEOREM, THE HOLDER-YOUNG-BRASCAMP-LIEB INEQUALITY, AND THE ASYMPTOTIC THEORY OF INTEGRALS AND QUADRATIC FORMS OF STATIONARY FIELDS |
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| Florin Avram 1Nikolai Leonenko 2 |
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| (17/03/2008) |
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| Many statistical applications require establishing central limit theorems for sums, integrals, or for quadratic forms of functions of a stationary process. A particularly important case is that of Appell polynomials, since the Appell expansion rank" determines typically the type of central limit theorem satisfied by these functionals. We review and extend here to multidimensional indices a functional analysis approach to this problem proposed by Avram and Brown (1989), based on the method of cumulants and on integrability assumptions in the spectral domain; several applications are presented as well. |
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| 1 : | Laboratoire de Mathématiques et de leurs Applications de Pau (LMA-PAU) |
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CNRS : UMR5142 – Université de Pau et des Pays de l'Adour [UPPA] |
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| 2 : | Cardiff School of Mathematics |
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Cardiff University |
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| 3 : | Dept. of Probability Theory and Mathematical Statistics |
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Kyiv National Taras Shevchenko University |
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| Domaine | : | Mathématiques/Probabilités |
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| hal-00264472, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00264472 | |
| oai:hal.archives-ouvertes.fr:hal-00264472 | |
| Contributeur : Florin Avram | |
| Soumis le : Lundi 17 Mars 2008, 12:39:28 | |
| Dernière modification le : Lundi 17 Mars 2008, 14:22:09 | |
