Isotropic Gaussian random fields on the sphere: regularity, fast simulation, and stochastic partial differential equations
Open access
Date
2013-05Type
- Report
ETH Bibliography
yes
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Abstract
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Loève 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 Hölder continuity and sample differentiability of the random fields is discussed. Rates of convergence of their finitely truncated Karhunen-Loève 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. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010386152Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
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 ratesOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Funding
247277 - Automated Urban Parking and Driving (EC)
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