Open Access
October, 2015 Smoothness of the joint density for spatially homogeneous SPDEs
Yaozhong HU, Jingyu HUANG, David NUALART, Xiaobin SUN
J. Math. Soc. Japan 67(4): 1605-1630 (October, 2015). DOI: 10.2969/jmsj/06741605


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 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, with some suitable regularity and nondegeneracy 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. "Smoothness of the joint density for spatially homogeneous SPDEs." J. Math. Soc. Japan 67 (4) 1605 - 1630, October, 2015.


Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 1334.60111
MathSciNet: MR3417506
Digital Object Identifier: 10.2969/jmsj/06741605

Primary: 60H15
Secondary: 60H07

Keywords: Malliavin calculus , smoothness of joint density , spatially homogeneous covariances , Stochastic partial differential equations , strict positivity

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 4 • October, 2015
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