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Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces. (English) Zbl 1456.60122

Summary: 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.

MSC:

60G60 Random fields
60G15 Gaussian processes
43A35 Positive definite functions on groups, semigroups, etc.
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