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

Annika Lang (Institutionen för matematiska vetenskaper, matematisk statistik) ; Ch. Schwab
The Annals of Applied Probability (1050-5164). Vol. 25 (2015), 6, p. 3047-3094.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: 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

Denna post skapades 2014-07-09. Senast ändrad 2016-01-20.
CPL Pubid: 200364


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)


Numerisk analys
Sannolikhetsteori och statistik

Chalmers infrastruktur