On the Asymptotic Behavior of the Prediction Error

Previous article Next article On the Asymptotic Behavior of the Prediction ErrorB. L. GolinskiiB. L. Golinskiihttps://doi.org/10.1137/1119079PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. A. Rozanov, Stationary random processes, Translated from the Russian by A. Feinstein, Holden-Day Inc., San Francisco, Calif., 1967vi+211 MR0214134 (35:4985) 0152.16302 Google Scholar[2] L. Ya. Geronimus, Orthogonal polynomials: Estimates, asymptotic formulas, and series of polynomials orthogonal on the unit circle and on an interval, Authorized translation from the Russian, Consultants Bureau, New York, 1961vi+242 MR0133643 (24:A3469) Google Scholar[3] Ulf Grenander and , Gabor Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley, 1958vii+245 MR0094840 (20:1349) 0080.09501 CrossrefGoogle Scholar[4] 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 MR0058902 (15,448e) 0059.11804 Google Scholar[5] Glen Baxter, An asymptotic result for the finite predictor, Math. Scand., 10 (1962), 137–144 MR0149584 (26:7069) 0112.09401 CrossrefGoogle Scholar[6] I. A. Ibragimov, On the asymptotic behavior of the prediction error, Theory Prob. Applications, 9 (1964), 627–634 10.1137/1109085 0146.40803 LinkGoogle Scholar[7] R. M. Trigub, The constructive characteristics of certain classes of functions, Izv. Akad. Nauk SSSR Ser. Mat., 29 (1965), 615–630, (In Russian.) MR0179531 (31:3779) Google Scholar[8] A. F. Timan, Theory of approximation of functions of a real variable, Translated from the Russian by J. Berry. English translation edited and editorial preface by J. Cossar. International Series of Monographs in Pure and Applied Mathematics, Vol. 34, A Pergamon Press Book. The Macmillan Co., New York, 1963xii+631 MR0192238 (33:465) 0117.29001 Google Scholar[9] Glen Baxter, A convergence equivalence related to polynomials orthogonal on the unit circle, Trans. Amer. Math. Soc., 99 (1961), 471–487 MR0126126 (23:A3422) 0116.35705 CrossrefGoogle Scholar[10] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959Vol. I. xii+383 pp.; Vol. II. vii+354 MR0107776 (21:6498) 0085.05601 Google Scholar[11] A. A. Konyuškov, Best approximations by trigonometric polynomials and Fourier coefficients, Mat. Sb. N.S., 44(86) (1958), 53–84, (In Russian.) MR0096074 (20:2571) Google Scholar[12] Ya. L. Geronimus, Polynomials orthogonal on a circle and their applications, Zapiski Naučno-Issled. Inst. Mat. Meh. Harkov. Mat. Obšč. (4), 19 (1948), 35–120, (Contributions of the Scientific Research Institute of Mathematics and Mechanics and Khar'kov Mathematical Society), (In Russian.) MR0036872 (12,176e) Google Scholar[13] G. Szegö, Orthogonal Polynomials, Colloquium Publications, Vol. 23, rev. ed. (Repr. of 1959 ed.), American Mathematical Society, Providence, R.I., 1967 Google Scholar[14] I. A. Ibragimov and , V. N. Solev, The asymptotic behavior of the prediction error of a stationary sequence with a spectral density of special type, Theory Prob. Applications, 13 (1968), 703–707 10.1137/1113089 0214.45402 LinkGoogle Scholar[15] B. L. Golinskii˘, An analogue of the Christoffel formula for polynomials orthogonal on the unit circle, and some applications, Izv. Vysš. Učebn. Zaved. Matematika, 1958 (1958), 33–42, (Transactions of the Higher Educational Establishment, Mathematics), (In Russian.) MR0131004 (24:A858) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Position and momentum information entropies of the D -dimensional harmonic oscillator and hydrogen atom1 October 1994 | Physical Review A, Vol. 50, No. 4 Cross Ref Volume 19, Issue 4| 1975Theory of Probability & Its Applications History Submitted:23 April 1973Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119079Article page range:pp. 693-709ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics