Conditions of Local Asymptotic Normality for Gaussian Stationary Processes

Let {bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let be the -algebra induced by the random variables {bold x}[], D(R¹), and let _t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by (f) the Gaussian measure on generated by {bold x}. Let _t(f) be the restriction of (f) to _t. Let f and g be nonnegative functions such that the measures _t(f) and _t(g) are absolutely continuous. Put For a fixed g(u) and for f(u)= f_t(u) close to g(u) in some sense, the asymptotic normality of _t(f,g) is proved under some regularity conditions. Bibliography: 14 titles.