论文标题
线性抛物线SPDE模型的参数估计在两个空间尺寸中，噪声较小
Parameter estimation for a linear parabolic SPDE model in two space dimensions with a small noise
论文作者
论文摘要
我们研究了两个空间维度的线性抛物线二阶随机偏微分方程（SPDE）的参数估计，其中使用高频数据与时间和空间相对于时间和空间，具有较小的分散参数。我们将两种类型的$ Q $ - 宇宙流程设置为驾驶噪音。我们根据空间中的数据稀薄数据提供了SPDE的系数参数的最小对比度估计值，并基于时间稀薄的数据近似坐标过程。此外，我们使用坐标过程是Ornstein-uhlenbeck过程和对扩散过程的统计推断，提出了漂移参数的估计值。
We study parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions with a small dispersion parameter using high frequency data with respect to time and space. We set two types of $Q$-Wiener processes as a driving noise. We provide minimum contrast estimators of the coefficient parameters of the SPDE appearing in the coordinate process of the SPDE based on the thinned data in space, and approximate the coordinate process based on the thinned data in time. Moreover, we propose an estimator of the drift parameter using the fact that the coordinate process is the Ornstein-Uhlenbeck process and statistical inference for diffusion processes with a small noise.
