# Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density

Abstract : In this paper we study a class of stochastic partial differential equations in the whole space $\mathbb{R}^{d}$, with arbitrary dimension $d\geq 1$, driven by a Gaussian noise white in time and correlated in space. The differential operator is a fractional derivative operator. We show the existence, uniqueness and H\"{o}lder's regularity of the solution. Then by means of Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure.
Type de document :
Article dans une revue
Osaka Journal of Mathematics, Osaka University, 2010, 47 (10), pp.41-65
Domaine :

https://hal.archives-ouvertes.fr/hal-00325068
Contributeur : Mohamed Mellouk <>
Soumis le : vendredi 26 septembre 2008 - 10:25:54
Dernière modification le : mercredi 12 octobre 2016 - 01:17:07

### Citation

Mohamed Mellouk. Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density. Osaka Journal of Mathematics, Osaka University, 2010, 47 (10), pp.41-65. <hal-00325068>

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