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

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

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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.

Information

Published: March 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1193.60081
MathSciNet: MR2666124

Subjects:
Primary: 60H15
Secondary: 35R60

Rights: Copyright © 2010 Osaka University and Osaka City University, Departments of Mathematics

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Vol.47 • No. 1 • March 2010
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