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Gaussian estimates of the density for systems of non-linear stochastic heat equations
Yinghui Shi, Xiaobin Sun · 2016-07-05 · via math.PR updates on arXiv.org

In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy conditions, the smoothness of the joint density of the solution for this system has been studied by E. Nualart in [11]. The purpose of this paper is further to study the lower and upper bounds of the density. The main tools are the Malliavin calculus and the method developed by Kohatasu-Higa in [6] or E. Nualart and Quer-Sardanyons in [12].

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