Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields - Deriev, I. I. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
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.