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| HAL : hal-00258033, version 1 |
| DOI : 10.1016/S0304-4149(99)00090-3 |
| Fiche détaillée |  Récupérer au format |
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| Stochastic Processes and their Applications 86, 1 (2000) 141-162 |
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| On a stochastic wave equation in two space dimension: regularity of the solution and its density |
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| Annie Millet 1, 2Pierre-Luc Morien 2 |
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| (03/2000) |
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| We pursue the investigation started in a recent paper by Millet and Sanz-Solé concerning a non-linear wave equation driven by a Gaussian white noise in time and correlated in the two-dimensional space variable. Under more restrictive conditions on the covariance function of the noise, we prove Hölder-regularity properties for both the solution and its density. For the latter, we adapt the method used in a paper by Morien based on the Malliavin calculus. |
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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 : | Modélisation aléatoire de Paris X (MODAL'X) |
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Université Paris X - Paris Ouest Nanterre La Défense |
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| PMA - MODAL'X |
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| Domaine | : | Mathématiques/Probabilités |
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| Stochastic partial differential equation – Wave equation – Gaussian noise – Malliavin calculus |
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| hal-00258033, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00258033 | |
| oai:hal.archives-ouvertes.fr:hal-00258033 | |
| Contributeur : Annie Millet | |
| Soumis le : Mercredi 20 Février 2008, 23:20:45 | |
| Dernière modification le : Jeudi 21 Février 2008, 00:30:25 | |
