论文标题
抛物线线性SPDE的自适应估计器，噪音很小
Adaptive estimator for a parabolic linear SPDE with a small noise
论文作者
论文摘要
我们根据高频数据，基于在时间和空间中观察到的高频率数据，处理抛物线线性线性二阶随机偏微分方程（SPDE）的参数估计。通过使用从高频数据获得的空间的稀薄数据，提出了SPDE两个系数参数的最小对比度估计器。对于从高频数据获得的时间，这些估计器和稀薄的数据，我们构建了SPDE的坐标过程的近似值。使用近似坐标过程，我们获得了SPDE系数参数的自适应估计器。此外，我们给出了SPDE提出的估计量的模拟结果。
We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned data with respect to space obtained from the high frequency data, the minimum contrast estimators of two coefficient parameters of the SPDE are proposed. With these estimators and the thinned data with respect to time obtained from the high frequency data, we construct an approximation of the coordinate process of the SPDE. Using the approximate coordinate process, we obtain the adaptive estimator of a coefficient parameter of the SPDE. Moreover, we give simulation results of the proposed estimators of the SPDE.
