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

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dc.creatorBoulanba, Lahcen
dc.creatorEddahbi, M'hamed
dc.creatorMellouk, Mohamed
dc.date2006-10-25
dc.date.accessioned2026-07-07T07:29:26Z
dc.date.available2026-07-07T07:29:26Z
dc.descriptionIn 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 Hölder'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.
dc.identifierhttps://arxiv.org/abs/math/0610769
dc.identifierhttp://arxiv.org/abs/math/0610769
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/118108
dc.subjectProbability
dc.subjectAnalysis of PDEs
dc.subject60H15; 35R60
dc.titleFractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density
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