Series representations and simulations of isotropic random fields in the Euclidean space

Ma, Z.; Ma, C.

doi:10.1090/tpms/1158

Authors: Z. Ma and C. Ma
Journal: Theor. Probability and Math. Statist. 105 (2021), 93-111
MSC (2020): Primary 60G60, 62M40; Secondary 33C10, 33C45
DOI: https://doi.org/10.1090/tpms/1158
Published electronically: December 7, 2021
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Abstract: This paper introduces the series expansion for homogeneous, isotropic and mean square continuous random fields in the Euclidean space, which involves the Bessel function and the ultraspherical polynomial, but differs from the spectral representation in terms of the ordinary spherical harmonics that has more terms at each level.The series representation provides a simple and efficient approach for simulation of isotropic (non-Gaussian) random fields.

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