SOJOURNS OF MULTIDIMENSIONAL GAUSSIAN RANDOM-FIELDS WITH DEPENDENT COMPONENTS

Asymptotic distributions are considered for functionals | {χ ε{lunate} υn (r) : ξ(χ) ε{lunate}νp (f(r))} |, n ≥ 1, p≥ 2, where υk(r) = {χ ε{lunate} Rk :| χ | < r } is a ball in Rk, |·| is the Lebesque measure, f : (0, ∞) → (0, ∞) is a nonrandom continuous function such that f(r) ↑ ∞, as r → ∞, and ξ(χ) = [ξ1(χ), ...,ξp(χ)]′ is a homogeneous isotropic vector Gaussian random field with strongly dependent components. © 1990.