期刊
ANNALS OF APPLIED PROBABILITY
卷 25, 期 6, 页码 3047-3094出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/14-AAP1067
关键词
Gaussian random fields; isotropic random fields; Karhunen-Loeve expansion; spherical harmonic functions; Kolmogorov-Chentsov theorem; sample Holder continuity; sample differentiability; stochastic partial differential equations; spectral Galerkin methods; strong convergence rates
资金
- ERC AdG [247277]
- Knut and Alice Wallenberg foundation
- European Research Council (ERC) [247277] Funding Source: European Research Council (ERC)
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Loeve 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 Holder continuity and sample differentiability of the random fields is discussed. Rates of convergence of their finitely truncated Karhunen-Loeve expansions in terms of the covariance spectrum are established, and algorithmic aspects of fast sample 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.
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