Abstract

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) < ∞ at some a > 0.

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19-25