Repository: Freie Universität Berlin, Math Department

Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere

Bachmayr, m: and Djurdjevac, A. (2020) Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere. : . (Submitted)

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Series expansions of isotropic Gaussian random fields on S2 with independent Gaussian coefficients and localized basis functions are constructed. Such representations provide an alternative to the standard Karhunen-Loève expansions of isotropic random fields in terms of spherical harmonics. Their multilevel localized structure of basis functions is especially useful in adaptive algorithms. 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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2490
Deposited By: Ulrike Eickers
Deposited On:17 Feb 2021 15:25
Last Modified:17 Feb 2021 15:25

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