We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types $Q$-Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the coordinate process 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.

翻译：我们考虑对两个空间维度的线性抛射二级局部偏差方程式的参数估计,这两个空间维度由基于时间和空间高频数据的两种“Q$-Wiener”进程驱动。我们首先使用基于空间数据薄度的最小对比度估计器来估计SPDE协调进程中出现的参数,然后构建SPDE的大致协调过程。此外,我们建议利用基于时间数据薄度的近似协调过程来估计SPDE的系数参数。我们还提供了一些模拟结果。