Regularity properties and simulation of Gaussian random fields on the sphere across time


Séminaire Probabilités & Statistique

9/03/2017 - 14:00 Jorge CLARKE (Université Paris Dauphine) Salle 106 - Batiment IMAG

In many geosciences applications, the phenomena of interest are observed on large portion
of the Planet Earth. When such phenomena evolves over time, a valid model for the study of these
observations is to consider them as partial realization of a spatio-temporal random field, where the
spatial component is defined on a sphere, considering this last as a more realistic representation of the
globe. We Introduce a family of Gaussian random fields constructed by spectral methods via a double
Karhunen-Loéve type representation. Based on later result on the literature we claim that this family
represent the class of Isotropic and stationary Gaussian random fields over Sd × R. In the formulation,
we exploit the theory about positive definite functions on the sphere and its extension to the spatio-
temporal context. We then study regularity properties of the proposed family via Sobolev spaces and
interpolation techniques. Then we approximate the elements of this family with a double truncation
and we analyse the accuracy of this technique evaluating the error in L2 -norm and through simulation

     Joint work with Alfredo Alegría and milio Porcu