论文标题
来自多个测量的线性SPDE的最佳参数估计
Optimal parameter estimation for linear SPDEs from multiple measurements
论文作者
论文摘要
二阶抛物线线性随机部分微分方程（SPDE）中的系数是从多个空间局部测量中估算的。假设空间分辨率趋于零并且测量数量不足，则每个系数的收敛速率取决于其差分顺序，并且对于高阶系数而言更快。基于对一般随机演化方程的繁殖核希尔伯特空间的明确分析，引入了高斯下限方案。结果，建立了最小值的速率以及足够和必要的条件以进行一致的估计。
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of measurements is non-decreasing, the rate of convergence for each coefficient depends on its differential order and is faster for higher order coefficients. Based on an explicit analysis of the reproducing kernel Hilbert space of a general stochastic evolution equation, a Gaussian lower bound scheme is introduced. As a result, minimax optimality of the rates as well as sufficient and necessary conditions for consistent estimation are established.
