To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

Isotropic Gaussian random… - University of Gothenburg, Sweden Till startsida
Sitemap
To content Read more about how we use cookies on gu.se

Isotropic Gaussian random fields on the sphere: regularity, fast simulation, and stochastic partial differential equations

Journal article
Authors Annika Lang
Ch. Schwab
Published in The Annals of Applied Probability
Volume 25
Issue 6
Pages 3047-3094
ISSN 1050-5164
Publication year 2015
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 3047-3094
Language en
Links dx.doi.org/10.1214/14-AAP1067
https://gup.ub.gu.se/file/178821
Keywords Gaussian random fields, isotropic random fields, Karhunen-Loève expansion, spherical harmonic functions, Kolmogorov-Chentsov theorem, sample Hölder continuity, sample differentiability, stochastic partial differential equations, spectral Galerkin methods, strong convergence rates
Subject categories Numerical analysis, Probability Theory and Statistics

Abstract

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.

Page Manager: Webmaster|Last update: 9/11/2012
Share:

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?