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：本文研究由两类$Q$-维纳过程驱动的二维空间线性抛物型二阶随机偏微分方程的参数估计问题，数据基于时间与空间的高频观测。我们提出基于时间与空间平方增量的系数参数最小对比估计量，并基于近似坐标过程给出系数参数的自适应估计量。此外，本文给出了所提估计量的示例及模拟结果。