Let {\bold x}[ċ] be a stationary Gaussian process with zero mean and spectral density f, let \documentclass[12pt]{minimal}
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$$\mathcal{F}$$
\end{document} be the σ-algebra induced by the random variables {\bold x}[ϕ], ϕ ∈ D(R1), and let \documentclass[12pt]{minimal}
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$$\mathcal{F}$$
\end{document}t, t > 0, be the σ-algebra induced by the random variables x[ϕ],supp ϕ ∈ [-t,t]. Denote by \documentclass[12pt]{minimal}
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$$\mathcal{P}$$
\end{document}(f) the Gaussian measure on \documentclass[12pt]{minimal}
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$$\mathcal{F}$$
\end{document} generated by {\bold x}. Let \documentclass[12pt]{minimal}
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$$\mathcal{P}$$
\end{document}t(f) be the restriction of \documentclass[12pt]{minimal}
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$$\mathcal{P}$$
\end{document}(f) to \documentclass[12pt]{minimal}
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$$\mathcal{F}$$
\end{document}t. Let f and g be nonnegative functions such that the measures \documentclass[12pt]{minimal}
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$$\mathcal{P}$$
\end{document}t(f) and \documentclass[12pt]{minimal}
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$$\mathcal{P}$$
\end{document}t(g) are absolutely continuous. Put \documentclass[12pt]{minimal}
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$$\mathcal{D}_t (f,g) = \log \frac{{d\mathcal{P}_t (f)}}{{d\mathcal{P}_t (g)}}.$$
\end{document} For a fixed g(u) and for f(u)= ft(u) close to g(u) in some sense, the asymptotic normality of \documentclass[12pt]{minimal}
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$$\mathcal{D}$$
\end{document}t(f,g) is proved under some regularity conditions. Bibliography: 14 titles.
