Regularity properties and simulations of Gaussian random fields on the Sphere cross Time

Jorge Clarke de La Cerda (1) , Alfredo Alegría (2) , Emilio Porcu (3, 2) , Jorge Clarke de La Cerda

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Newcastle University, School of Mathematics and Statistics
3 Deparamento de Matematica

We study the regularity properties of Gaussian fields defined over spheres across time. In particular, we consider two alternative spectral decompositions for a Gaussian field on S d × R. For each decomposition, we establish regularity properties through Sobolev and interpolation spaces. We then propose a simulation method and study its level of accuracy in the L 2 sense. The method turns to be both fast and efficient.

Mots clés: Schoenberg's functions; Spherical harmonics functions; Global data; Space-time covariance; Big data; Gaussian random fields; Karhunen-Lóeve expansion

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Jorge Clarke de La Cerda, Alfredo Alegría, Emilio Porcu, Jorge Clarke de La Cerda. Regularity properties and simulations of Gaussian random fields on the Sphere cross Time. Electronic Journal of Statistics , In press. ⟨hal-01394121v2⟩