Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density
Boulanba, Lahcen ; Eddahbi, M'hamed ; Mellouk, Mohamed
Osaka J. Math., Tome 47 (2010) no. 1, p. 41-65 / Harvested from Project Euclid
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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.
Publié le : 2010-03-15
Classification:  60H15,  35R60 
@article{1266586785,
     author = {Boulanba, Lahcen and Eddahbi, M'hamed and Mellouk, Mohamed},
     title = {Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density},
     journal = {Osaka J. Math.},
     volume = {47},
     number = {1},
     year = {2010},
     pages = { 41-65},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1266586785}
}

Boulanba, Lahcen; Eddahbi, M'hamed; Mellouk, Mohamed. Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density. Osaka J. Math., Tome 47 (2010) no. 1, pp.  41-65. http://gdmltest.u-ga.fr/item/1266586785/