Conditions of Local Asymptotic Normality for Gaussian Stationary Processes |
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Authors: | V N Solev A Zerbet |
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Institution: | (1) St.Petersburg Department of the, Steklov Mathematical Institute, Russia;(2) Bordeaux-2, France |
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Abstract: | 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)= ft(u) close to g(u) in some sense, the asymptotic normality of
t(f,g) is proved under some regularity conditions. Bibliography: 14 titles. |
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Keywords: | |
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