Applied Analysis Seminar - Abstracts
Talk
Thursday, 5 December 2019, 13:30-14:30 in HG02.052
Sonja Cox (Universiteit van Amsterdam)
Simulation of non-stationary Gaussian fields: convergence in Hölder and Sobolov norms.
Abstract
In models involving a Gaussian field one frequently assumes the covariance
operator to be given by a negative fractional power of a second-order
elliptic differential operator of the form L:= -∇·(A∇) + κ².
Whittle-Matérn fields form an well-known example of such a model. Such
covariance operators allow for a reasonable amount of model flexibility
(adjustable correlation length and the smoothness of the field) whilst
being relatively easy to simulate. Most importantly, they allow for the
simulation of non-stationary random fields.
In our work we established optimal strong convergence rates in Hölder
and Sobolov norms for Galerkin approximations of such Gaussian random
fields. More specifically, we considered both spectral Galerkin methods
and finite element methods. The latter, although significantly more
tedious to analyse, are more suitable for non-stationary fields on non-standard domains.
The talk concerns joint work with Kristin Kirchner (ETHZ).
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