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 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.
Citation
Lahcen Boulanba. M'hamed Eddahbi. Mohamed Mellouk. "Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density." Osaka J. Math. 47 (1) 41 - 65, March 2010.
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