Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces

Galatia Cleanthous, Athanasios G. Georgiadis, Annika Lang and Emilio Porcu

Stochastic Processes and their Applications, 2020, vol. 130, issue 8, 4873-4891

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.

Keywords: Angular power spectrum; Approximation; Compact two-point homogeneous spaces; Covariance kernel; Hölder regularity; Random fields (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.02.003

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