Abstract
This paper is an extension of [11]. Starting from the results of our first paper we prove by inclusion theorems that bounds for the correlation function of a stationary Gaussian process in the space of continuous functions with weight are strongly consistent and asymptotically normal. We construct the simplest functional confidence intervals in these spaces for the indeterminate correlation function.
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V. V. Buldygin and V. V. Zayats, “Asymptotic properties of correlation bounds in function spaces. I,” Ukr. Mat. Zh.,43, No. 2, 179–187 (1991).
V. V. Buldygin and V. V. Zayats, Asymptotic Properties of Bounds for Correlation of a Uniform Gaussian Random Field in Functional Hilbert Spaces, Kiev (1990) (Preprint Akad. Nauk Ukr. SSR, Inst. Mat., No. 90.5).
V. V. Buldygin, Convergence of Random Processes in Topological Spaces, Naukova Dumka (1980).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 322–329, March, 1991.
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Buldygin, V.V., Zayats, V.V. Asymptotic properties of correlation bounds in functional spaces. II. Ukr Math J 43, 286–292 (1991). https://doi.org/10.1007/BF01670067
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DOI: https://doi.org/10.1007/BF01670067