We consider the stochastic heat equation driven by a multiplicative Gaussian noise that is white in time and spatially homogeneous in space. Assuming that the spatial correlation function is given by a Riesz kernel of order $\alpha \in (0,1)$, we prove a central limit theorem for power variations and other related functionals of the solution. To our surprise, there is no asymptotic bias despite the low regularity of the noise coefficient in the multiplicative case. We trace this circumstance back to cancellation effects between error terms arising naturally in second-order limit theorems for power variations.

翻译：我们研究了由乘性高斯噪声驱动的随机热方程，该噪声在时间上为白噪声且在空间上均匀。假设空间相关函数由阶数为$\alpha \in (0,1)$的Riesz核给出，我们证明了该解的幂变差及其他相关泛函的中心极限定理。令人惊讶的是，尽管在乘性情形下噪声系数具有低正则性，却未出现渐近偏差。我们将此现象归因于幂变差二阶极限定理中自然产生的误差项之间的抵消效应。