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Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions
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We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with the quadratic covariation of the latent random process that drives the evolution equation which is assumed to be a Hilbert space-valued semimartingale. We discuss applications to dynamically consistent and outlier-robust dimension reduction in the spirit of functional principal components and the estimation of infinite-dimensional stochastic volatility models.
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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.
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