We deal with parameter estimation for a linear parabolic second-order stochastic partial differential equation in two space dimensions driven by two types of $Q$-Wiener processes based on high frequency data with respect to time and space. We propose minimum contrast estimators of the coefficient parameters based on temporal and spatial squared increments, and provide adaptive estimators of the coefficient parameters based on an approximate coordinate process. We also give an example and simulation results of the proposed estimators.
翻译:本文研究了线性抛物型二阶随机偏微分方程的参数估计问题,该方程在两个空间维度上由两种$Q$-Wiener过程驱动,并且采用高频时间和空间数据。我们提出了基于时间和空间平方增量的最小对比度估计器,并提供了近似坐标过程的自适应估计器的系数参数。我们还给出了一个例子和所提出估计器的模拟结果。