Том 71
№ 11

All Issues

Deriev I. I.

Articles: 1
Article (Russian)

Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields

Deriev I. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 472–480

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.