标题： 基于时空填充渐近的抛物型SPDE中噪声协方差核的非参数推断 显示英文标题

标题： Nonparametric Inference for Noise Covariance Kernels in Parabolic SPDEs using Space-Time Infill-Asymptotics

摘要： 我们为使用时空内插渐近方法在具有加性彩色噪声的线性抛物型随机偏微分方程（SPDEs）中对噪声协方差核进行非参数估计，发展了一种渐近极限理论。 该方法采用离散化的无限维实现协方差，并仅需要对核的轻微正则性假设以确保估计量的一致性和渐近正态性。 在此基础上，我们构建了与SPDE的微分算子无关的噪声协方差的整体拟合优度检验。 我们的框架能够适应各种空间采样方案，并允许在空间分辨率低于时间分辨率的情况下进行可靠推断。 显示英文摘要

摘要： We develop an asymptotic limit theory for nonparametric estimation of the noise covariance kernel in linear parabolic stochastic partial differential equations (SPDEs) with additive colored noise, using space-time infill asymptotics. The method employs discretized infinite-dimensional realized covariations and requires only mild regularity assumptions on the kernel to ensure consistent estimation and asymptotic normality of the estimator. On this basis, we construct omnibus goodness-of-fit tests for the noise covariance that are independent of the SPDE's differential operator. Our framework accommodates a variety of spatial sampling schemes and allows for reliable inference even when spatial resolution is coarser than temporal resolution.