{"ID":2877265,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.20947","arxiv_id":"2508.20947","title":"Nonparametric Inference for Noise Covariance Kernels in Parabolic SPDEs using Space-Time Infill-Asymptotics","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.","short_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...","url_abs":"https://arxiv.org/abs/2508.20947","url_pdf":"https://arxiv.org/pdf/2508.20947v1","authors":"[\"Andreas Petersson\",\"Dennis Schroers\"]","published":"2025-08-28T16:09:08Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}