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arXiv · 2508.20947

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

Andreas Petersson·Dennis Schroers
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Abstract

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.

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Andreas Petersson, Dennis Schroers. 2025-08-28. Nonparametric Inference for Noise Covariance Kernels in Parabolic SPDEs using Space-Time Infill-Asymptotics. https://arxiv.org/abs/2508.20947

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