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| HAL : hal-00619049, version 2 |
| arXiv : 1109.0838 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (05-09-2011) | v2 (11-07-2012) |
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| A central limit theorem for stationary random fields |
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Mohamed El Machkouri 1Dalibor Volny 1 |
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| (29/06/2012) |
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| This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k = g\left(\varepsilon_{k-s}, s \in \Z^d \right)$, $k\in\Z^d$, where $(\varepsilon_i)_{i\in\Z^d}$ are i.i.d random variables and $g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established. |
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| 1 : | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
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CNRS : UMR6085 – Université de Rouen |
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| 2 : | Department of Mathematics |
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University of Chicago |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie |
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| Central limit theorem – spatial processes – m-dependent random fields – weak mixing. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00619049, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00619049 | |
| oai:hal.archives-ouvertes.fr:hal-00619049 | |
| Contributeur : Mohamed EL MACHKOURI | |
| Soumis le : Mardi 10 Juillet 2012, 23:42:42 | |
| Dernière modification le : Mercredi 11 Juillet 2012, 08:05:34 | |
