论文标题
基于高频数据的两个空间维度的线性抛物线SPDE的参数估计
Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data
论文作者
论文摘要
我们考虑在两个空间维度中，由两种类型的$ q $ - WIENER过程驱动的两个空间维度的线性二阶随机偏微分方程（SPDE）的参数估计。我们首先使用最小对比度估计器基于相对于空间的稀薄数据来估算SPDE中出现的参数，然后构建SPDE的近似坐标过程。此外，我们提出了SPDE系数参数的估计值，该估计基于时间上的数据，利用近似坐标过程。我们还提供了一些模拟结果。
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.
