Series representations and simulations of isotropic random fields in the Euclidean space
Ma, Z. Ma, Chunsheng
Ma, Z.
Ma, Chunsheng
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2021-12-07
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Article
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Keywords
Bessel function,Covariance function,Isotropy,Random field,Ultraspherical polynomials
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Citation
Ma, Z., & Ma, C. (2021). Series representations and simulations of isotropic random fields in the Euclidean space. Theory of Probability and Mathematical Statistics, 105, 93-111.
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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American Mathematical Society
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Theory of Probability and Mathematical Statistics
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1547-7363