Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations
Artikel i vetenskaplig tidskrift, 2015

Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`eve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample H\"older continuity and sample differentiability of the random fields is discussed. Rates of convergence of their finitely truncated Karhunen-Lo\`eve expansions in terms of the covariance spectrum are established, and algorithmic aspects of fast sample path generation via fast Fourier transforms on the sphere are indicated. The relevance of the results on sample regularity for isotropic Gaussian random fields and the corresponding lognormal random fields on the sphere for several models from environmental sciences is indicated. Finally, the stochastic heat equation on the sphere driven by additive, isotropic Wiener noise is considered and strong convergence rates for spectral discretizations based on the spherical harmonic functions are proven.

sample Hölder continuity

Karhunen-Loève expansion

Gaussian random fields

sample differentiability

stochastic partial differential equations

spectral Galerkin methods

Kolmogorov-Chentsov theorem

spherical harmonic functions

isotropic random fields

strong convergence rates

Författare

Annika Lang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Ch. Schwab

Chalmers University of Technology

Annals of Applied Probability

1050-5164 (ISSN)

Vol. 25 3047-3094

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper

DOI

10.1214/14-AAP1067