Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere

2020/11/13 by Markus Bachmayr, Bachmayr, Markus, Ana Djurdjevac +1
Environmental Science · #43A90 #60G15 #60G60 #65T99 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Soil Geostatistics and Mapping

paper · pdf · doi:10.48550/arxiv.2011.06987

openalex publication_date 2020/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Series expansions of isotropic Gaussian random fields on \mathbbS² with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to the standard Karhunen-Loève expansions of isotropic random fields in terms of spherical harmonics. The basis functions are obtained by applying the square root of the covariance operator to spherical needlets. Localization of the resulting covariance-dependent multilevel basis is shown under decay conditions on the angular power spectrum of the random field. In addition, numerical illustrations are given and an application to random elliptic PDEs on the sphere is analyzed.

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