Characterization Theorems for Covariance Functions on the n−Dimensional Sphere Across Time

Anne Estrade (1) , Alessandra Fariñas (2) , Emilio Porcu (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 Deparamento de Matematica

This paper provides representation theorems for classes of nonstationary covariance functions on spheres across time. Isotropy on spheres comes out naturally in virtue of the addition theorem, and we show how to escape from this assumption, in order to obtain kernels that can be anisotropic. The same criterion is used in order to escape from stationarity in the temporal component. Our findings are then illustrated through a simulation study.

Mots clés: Positive definite kernel; Spherical harmonics; Gegenbauer polynomials; Spectral representation; Space-time random fields

Domaines: Mathématiques [math]; Statistiques [stat]

Anne Estrade, Alessandra Fariñas, Emilio Porcu. Characterization Theorems for Covariance Functions on the n−Dimensional Sphere Across Time. 2016. ⟨hal-01417668v1⟩