Seminar in Numerical Analysis: Kristin Kirchner (ETH Zürich)

Numerical methods for fractional PDEs with applications to spatial statistics

Many models in spatial statistics are based on Gaussian Matérn fields. Motivated by the relation between this class of Gaussian random fields and stochastic partial differential equations (PDEs), we consider the numerical solution of fractional-order elliptic stochastic PDEs with additive spatial white noise on a bounded Euclidean domain.

We propose an approximation supported by a rigorous error analysis which shows different notions of convergence at explicit and sharp rates. We furthermore discuss the computational complexity of the proposed method. Finally, we present several numerical experiments, which attest the theoretical outcomes, as well as a statistical application where we use the method for inference, i.e., for parameter estimation given data, and for spatial prediction.

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