Limit distributions of certain functionals of homogeneous isotropic Gaussian fields with strong dependency (Q1120899)

[For the entire collection of the original see Zbl 0626.00025.] The paper investigates the limit distributions of functionals \[ V_ 1(r)=2^{-1}\int_{\{| x| \leq r\}}\{\eta (x)+| \zeta (x)| \}dx,\quad V_ 2(r)=\int_{\{| x| \leq r\}}| \zeta (x)| dx \] and of some others of geometric type, generated by realizations of Gaussian homogeneous isotropic random fields \(\zeta\) (x), with covariance B(\(| x|)\) weakly converging to zero for \(| x| \to \infty\) (long range dependence). The problem is solved by reduction to the univariate case, so that limit distributions are not always Gaussian.