Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields
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.
English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 4, pp 503-512.
Citation Example: Deriev I. I. Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields // Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 472–480.