Bispectrum and a non-linear model for a non-Gaussian homogenous and isotropic field in 3D

Terdik, György; Nádai, László

doi:10.1090/tpms/1027

Bispectrum and a non-linear model for a non-Gaussian homogenous and isotropic field in 3D

Authors: György Terdik and László Nádai
Journal: Theor. Probability and Math. Statist. 95 (2017), 153-172
MSC (2010): Primary 60G60, 62M15; Secondary 62M30
DOI: https://doi.org/10.1090/tpms/1027
Published electronically: February 28, 2018
MathSciNet review: 3631649
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Abstract: The so-called bispectrum is a widely used construction for analyzing non-linear time series. In this paper the generalized bispectrum of a homogenous and isotropic stochastic field in 3D is introduced. The isotropy is considered in third order, and we give some necessary and sufficient conditions for isotropy of homogenous random fields. The spatial three-point correlation function (bicovariance function) is given by the bispectrum in terms of a kernel function, which is a superposition of spherical Bessel-functions and Legendre-polynomials. In return, the same kernel function is used in expressing the bispectrum by the bicovariance function. As an example, we generalize a model for non-Gaussian fields, which is the sum of a Gaussian field and its 2nd degree Hermite-polynomial. This model can be applied as an alternative to the Gaussian one used in Cosmology for non-Gaussian CMB temperature fluctuations.

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