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arXiv · 1410.1581

Smoothness of the joint density for spatially homogeneous SPDEs

Yaozhong Hu·Jingyu Huang·David Nualart·Xiaobin Sun
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Abstract

In this paper we consider a general class of second order stochastic partial differential equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and it has a homogeneous spatial covariance. Using the techniques of Malliavin calculus we derive the smoothness of the density of the solution at a fixed number of points $(t,x_1), \dots, (t,x_n)$, $t>0$, assuming some suitable regularity and non degeneracy assumptions. We also prove that the density is strictly positive in the interior of the support of the law.

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Yaozhong Hu, Jingyu Huang, David Nualart, Xiaobin Sun. 2014-10-06. Smoothness of the joint density for spatially homogeneous SPDEs. https://arxiv.org/abs/1410.1581

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