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

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

2006-10-25

arxiv.org/abs/math/0610769v1

Mathematics

Probability

Scientific paper

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.

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