On Asymptotic Behavior of the Prediction Error in the Singular Case

Previous article Next article On Asymptotic Behavior of the Prediction Error in the Singular CaseN. M. BabayanN. M. Babayanhttps://doi.org/10.1137/1129018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Murray Rosenblatt, Some purely deterministic processes, J. Rat. Mech. Anal., 6 (1957), 801–810 Google Scholar[2] Ulf Grenander and , Murray Rosenblatt, An extension of a theorem of G. Szegö and its application to the study of stochastic processes, Trans. Amer. Math. Soc., 76 (1954), 112–126 15,448e 0059.11804 Google Scholar[3] Stefan Mazurkiewicz, Un théorème sur les polynômes, Ann. Soc. Polon. Math., 18 (1945), 113–117 8,266d 0061.14404 Google Scholar[4] Glen Baxter, An asymptotic result for the finite predictor, Math. Scand., 10 (1962), 137–144 26:7069 0112.09401 CrossrefGoogle Scholar[5] I. A. Ibragimov, On the asymptotic behaviour of the prediction error, Theory Prob. Appl., 9 (1964), 627–634 0146.40803 LinkGoogle Scholar[6] Ya. L. Geronimus, On certain asymptotic properties of polynomials, Mat. Sbornik N. S., 23(65) (1948), 77–88, (In Russian.) 10,190g Google Scholar[7] A. G. Szegö, Orthogonal Polynomials, American Mathematical Society, New York, 1955 Google Scholar[8] U. Grenander and , A. G. Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley, 1958vii+245 20:1349 0080.09501 CrossrefGoogle Scholar[9] G. M. Goluzin, The Geometrical Theory of Functions of a Complex Variable, Nauka, Moscow, 1966628 pp. (1 plate; errata insert), (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails ON ASYMPTOTIC BEHAVIOR OF THE PREDICTION ERROR FOR A CLASS OF DETERMINISTIC STATIONARY SEQUENCES25 July 2022 | Acta Mathematica Hungarica, Vol. 167, No. 2 Cross Ref Extensions of Rosenblatt's results on the asymptotic behavior of the prediction error for deterministic stationary sequences27 December 2020 | Journal of Time Series Analysis, Vol. 42, No. 5-6 Cross Ref On Hyperbolic Decay of Prediction Error Variance for Deterministic Stationary Sequences1 September 2020 | Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), Vol. 55, No. 2 Cross Ref On exponential decay of the variance of BLUE for the mean of a stationary sequenceStudia Scientiarum Mathematicarum Hungarica, Vol. 56, No. 4 Cross Ref Asymptotic Behavior of the Variance of the Best Linear Unbiased Estimator for the Mean of a Discrete-time Singular Stationary Process27 December 2019 | Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), Vol. 54, No. 6 Cross Ref Capacity Results for Block-Stationary Gaussian Fading Channels With a Peak Power ConstraintIEEE Transactions on Information Theory, Vol. 53, No. 12 Cross Ref Capacity Results for Block-Stationary Gaussian Fading Channels Cross Ref Volume 29, Issue 1| 1985Theory of Probability & Its Applications History Submitted:10 April 1981Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1129018Article page range:pp. 147-150ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics