Optimal parameter estimation for linear SPDEs from multiple measurements
研究了从多次空间局部测量中估计二阶抛物型线性随机偏微分方程系数的问题，发现系数收敛速度与其微分阶数正相关，并建立了极小化最优速率和一致估计的充要条件。
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 nondecreasing, 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.