We consider parameter estimation of the reaction term for a second order linear parabolic stochastic partial differential equation in two space dimensions driven by a $Q$-Wiener process under small diffusivity. We first construct an estimator of the reaction parameter based on continuous spatio-temporal data, and then derive an estimator of the reaction parameter based on high frequency spatio-temporal data by discretizing the estimator based on the continuous data. We show that the estimators have consistency and asymptotic normality. Furthermore, we give simulation results of the estimator based on high frequency data.

翻译：本文研究在二维空间中由$Q$-维纳过程驱动的二阶线性抛物型随机偏微分方程在小扩散率条件下的反应项参数估计问题。我们首先基于连续时空数据构造反应参数估计量，随后通过对连续数据估计量进行离散化，推导出基于高频时空数据的反应参数估计量。研究表明，所提出的估计量具有相合性和渐近正态性。此外，我们给出了基于高频数据估计量的数值模拟结果。