Series representations and simulations of isotropic random fields in the Euclidean space. (English) Zbl 1493.60084
Summary: 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.
MSC:
| 60G60 | Random fields |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
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