Realized covariations from discrete space-time data consistently estimate the noise covariance kernel of a parabolic SPDE in Hilbert-Schmidt norm, with rates and tests, even when the differential operator is unknown.
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Nonparametric Inference for Noise Covariance Kernels in Parabolic SPDEs using Space-Time Infill-Asymptotics
Realized covariations from discrete space-time data consistently estimate the noise covariance kernel of a parabolic SPDE in Hilbert-Schmidt norm, with rates and tests, even when the differential operator is unknown.