1987•Theory of Probability and Its ApplicationsRequires access
The Law of the Iterated Logarithm for Weighted Sums of Independent Identically Distributed Random Variables
Oleg Ivanovich Klesov
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Abstract
Previous article Next article The Law of the Iterated Logarithm for Weighted Sums of Independent Identically Distributed Random VariablesO. I. KlesovO. I. Klesovhttps://doi.org/10.1137/1131043PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Kolmogorov, Über das Gesetz des iterierten Logarithmus, Math. Ann., 101 (1929), 126–135 CrossrefGoogle Scholar[2] V. A. Egorov, On Kolmogorov's theorem on the law of the iterated logarithm, Vestnik Leningrad. Univ., (1972), 140–142, 153, (In Russian.) 48:7350 Google Scholar[3] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346, Berlin–Heidelberg 52:9335 0322.60042 CrossrefGoogle Scholar[4] V. A. Egorov, On the law of the iterated logarithm, Theory Probab. Appl., 14 (1969), 693–699 10.1137/1114086 0211.48903 LinkGoogle Scholar[5] Y. S. Chow and , H. Teicher, Iterated logarithm laws for weighted averages, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 26 (1973), 87–94 48:9821 0298.60015 CrossrefGoogle Scholar[6] A. I. Martikainen, On the law of the iterated logarithm for weighted and perturbed sums, Theory Probab. Appl., 23 (1978), 362–365 10.1137/1123038 LinkGoogle Scholar[7] Philip Hartman and , Aurel Winter, On the law of the iterated logarithm, Amer. J. Math., 63 (1941), 169–176 2,228h 0024.15802 CrossrefGoogle Scholar[8] A. Bikyalis, Estimates of the remainder term in the central limit theorem, Litovsk. Mat. Sb., 6 (1966), 323–346, (In Russian.) 35:1067 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Exact bounds for the rate of convergence in general stochastic approximation procedures3 April 2007 | Stochastic Analysis and Applications, Vol. 16, No. 3 Cross Ref Recursive Estimation and Difference Equations28 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 2AbstractPDF (403 KB) Volume 31, Issue 2| 1987Theory of Probability & Its Applications History Submitted:15 June 1984Published online:03 August 2006 InformationCopyright © 1987 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131043Article page range:pp. 337-342ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics