We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types of $Q$-Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the eigenfunctions of the differential operator of the SPDE using the minimum contrast estimator based on the thinned data with respect to space, and then construct an approximate coordinate process of the SPDE. Furthermore, we propose estimators of the coefficient parameters of the SPDE utilizing the approximate coordinate process based on the thinned data with respect to time. We also give some simulation results.

中文翻译：

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基于高频数据的二维空间线性抛物型SPDE参数估计

我们考虑由两种类型驱动的二维空间中线性抛物型二阶随机偏微分方程 (SPDE) 的参数估计$问$-基于时间和空间上的高频数据的维纳处理。我们首先使用基于空间细化数据的最小对比度估计器来估计SPDE微分算子特征函数中出现的参数，然后构造SPDE的近似坐标过程。此外，我们提出了利用基于相对于时间的细化数据的近似坐标过程的 SPDE 系数参数的估计器。我们还给出了一些模拟结果。