Regularity,continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces |
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Affiliation: | Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, S–412 96 Göteborg, Sweden |
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Abstract: | Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided. |
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Keywords: | Angular power spectrum Approximation Compact two-point homogeneous spaces Covariance kernel Hölder regularity Random fields |
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