SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5422-5440, January 2020.
We study the solution to a nonlinear stochastic heat equation in $d\geq 3$. The equation is driven by a Gaussian multiplicative noise that is white in time and smooth in space. For a small coupling constant, we prove (i) that the solution converges to the stationary distribution in large time and (ii) that the diffusive scale fluctuations are described by the Edwards--Wilkinson equation.

中文翻译：

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三维和更高维非线性随机热方程的涨落

SIAM数学分析杂志，第52卷，第6期，第5422-5440页，2020年1月。
我们研究了$ d \ geq 3 $中非线性随机热方程的解。该方程由时间为白色且空间为平滑的高斯乘法噪声驱动。对于较小的耦合常数，我们证明（i）长时间内解收敛于平稳分布，以及（ii）扩散标度波动由Edwards-Wilkinson方程描述。