Weak convergence of randomized spectral models of Gaussian random vector fields

Convergence of randomized spectral models of homogeneous vector fields is studied in the sense of convergence in distribution in a uniform metric of the Banach space of continuous functions. Under quite moderate restrictions on the parameters of the spectral model, weak convergence to a Gaussian field is shown if the spectral density p(λ) of this field satisfies the condition ∫[ln(1 + |λ|)]1+ap(λ)dλ < ∞ at some a > 0.