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| HAL : hal-00111189, version 1 |
| arXiv : math.PR/0611090 |
| DOI : 10.1023/B:JOTP.0000020474.79479.fa |
| Fiche détaillée |  Récupérer au format |
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| Journal of Theoretical Probability 17 (2004) 1-49 |
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| On strongly Petrovskii's parabolic SPDEs in arbitrary dimension and the stochastic Cahn-Hilliard equation |
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| Caroline Cardon-Weber 1Annie Millet 1, 2, 3 |
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| (01/2004) |
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| In this paper we show that the Cahn-Hilliard stochastic SPDE has a function valued solution in dimension 4 and 5 when the perturbation is driven by a space-correlated Gaussian noise. This is done proving general results on SPDEs with globally Lipschitz coefficients associated with operators on smooth domains of $\mathbb{R}^d$ which are parabolic in the sense of Petrovskii}, and do not necessarily define a semi-group of operators. We study the regularity of the trajectories of the solutions and the absolute continuity of the law at some given time and position. |
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| 1 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| 2 : | Statistique Appliquée et MOdélisation Stochastique (SAMOS) |
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Université Paris I - Panthéon Sorbonne |
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| 3 : | Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques (MATISSE) |
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CNRS : UMR8595 – Université Paris I - Panthéon Sorbonne |
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| SAMOS-MATISSE http://samos.univ-paris1.fr |
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| Domaine | : | Mathématiques/Probabilités |
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| Parabolic operators – Cahn-Hilliard equation – Green function – SPDEs – Malliavin calculus |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00111189, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00111189 | |
| oai:hal.archives-ouvertes.fr:hal-00111189 | |
| Contributeur : Annie Millet | |
| Soumis le : Vendredi 3 Novembre 2006, 18:28:51 | |
| Dernière modification le : Mercredi 7 Février 2007, 17:37:34 | |
