Abstract
The central limit theorem is proved for the integral-type functionals of nonlinear transformations of two-and three-dimensional uniform isotropic Gaussian random fields. A theorem on convergence of finite-dimensional distributions of these functionals to the corresponding distributions of the Wiener process is also established.
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References
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 472–480, April, 1993.
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Deriev, I.I. Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields. Ukr Math J 45, 503–512 (1993). https://doi.org/10.1007/BF01062946
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DOI: https://doi.org/10.1007/BF01062946