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Nonstationary Space-time Covariance Functions induced by Dynamical Spatial Diffeomorphisms

Rachid Senoussi (INRAE BioSP)
Modeling nonstationarity in spatial and space-time processes is a major challenge that has been faced from several perspectives. Our presentation proposes a novel approach to tackle non-stationarity by considering a bridge between ordinary differential equations and homogeneous random fields. Specifically, we consider dynamical deformations of the spatial support of a stationary random field induced by certain classes of ordinary differential equations (over d-dimensional Euclidean spaces and hyperspheres) leading in general to the loss of the initial stationarity property. We conclude the presentation by showing the performance of the maximum likelihood estimation of the parameters of a specific family of dynamically deformed covariance structure of a Gaussian field over the usual sphere.
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