On The Spectrum Of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition I. Necessary Conditions

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Previous article Next article On The Spectrum Of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition I. Necessary ConditionsI. A. IbragimovI. A. Ibragimovhttps://doi.org/10.1137/1110008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov, On stationary Gaussian processes with a strong mixing property, Dokl. Akad. Nauk SSSR, 147 (1962), 1282–1284, (In Russian.) MR0144378 0129.30102 Google Scholar[2] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U. S. A., 42 (1956), 43–47 MR0074711 0070.13804 CrossrefGoogle Scholar[3] A. N. Kolmogorov and , Yu. A. Rozanov, On strong mixing conditions for stationary Gaussian processes, Theory Prob. Applications, 5 (1960), 240–208, (English translation.) LinkGoogle Scholar[4] A. N. Kolmogorov, Stationary sequences in Hilbert space, Bull. Moscow Univ., 2 (1941), 1–40, (In Russian.) 0063.03291 Google Scholar[5] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[6] V. P. Leonov, On the variance of time averages of stationary stochastic processes, Theory Prob. Applications, 6 (1961), 87–93, (English translation.) 10.1137/1106007 0128.12701 LinkGoogle Scholar[7] A. M. Yaglom, On linear interpolation for stationary random variables and processes, Uspekhi Mat. Nauk, IV (1949), 171–178, (In Russian.) Google Scholar[8] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949xvi+396 MR0030620 0032.05801 Google Scholar[9] A. Zygmund, Smooth functions, Duke Math. J., 12 (1945), 47–76 10.1215/S0012-7094-45-01206-3 MR0012691 0060.13806 CrossrefGoogle Scholar[10] N. K. Bari, A treatise on trigonometric series. Vols. I, II, Authorized translation by Margaret F. Mullins. A Pergamon Press Book, The Macmillan Co., New York, 1964Vol. I: xxiii+553 pp. Vol. II: xix+508, (English translation.) MR0171116 0129.28002 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Optimum Performance of Short Block Length Codes Under Multivariate Stationary Rayleigh FadingIEEE Transactions on Wireless Communications, Vol. 19, No. 3 | 1 Mar 2020 Cross Ref Uniform FIR approximation of causal Wiener filters, with applications to causal coherenceSignal Processing, Vol. 122 | 1 May 2016 Cross Ref Mixed-Norm Spaces and Prediction of S α S Moving AveragesJournal of Time Series Analysis, Vol. 36, No. 6 | 27 April 2015 Cross Ref Rate of Convergence in Approximating the Spectral Factor of Regular Stochastic SequencesIEEE Transactions on Information Theory, Vol. 55, No. 12 | 1 Dec 2009 Cross Ref A parametric bootstrap test for cyclesJournal of Econometrics, Vol. 129, No. 1-2 | 1 Nov 2005 Cross Ref Model selection for (auto-)regression with dependent dataESAIM: Probability and Statistics, Vol. 5 | 15 August 2002 Cross Ref The mixing rate of a stationary multivariate processJournal of Theoretical Probability, Vol. 6, No. 3 | 1 Jul 1993 Cross Ref Rational spectral densities and strong mixingJournal of Multivariate Analysis, Vol. 42, No. 2 | 1 Aug 1992 Cross Ref On the Spectrum of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition. II. Sufficient Conditions. Mixing RateI. A. IbragimovTheory of Probability & Its Applications, Vol. 15, No. 1 | 17 July 2006AbstractPDF (1018 KB) Volume 10, Issue 1| 1965Theory of Probability & Its Applications1-192 History Submitted:26 June 1964Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110008Article page range:pp. 85-106ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics