On a Relation Between an Estimate of the Remainder in the Central Limit Theorem and the Law of the Iterated Logarithm

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Previous article Next article On a Relation Between an Estimate of the Remainder in the Central Limit Theorem and the Law of the Iterated LogarithmV. V. PetrovV. V. Petrovhttps://doi.org/10.1137/1111046PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Kolmogoroff, Über das Gesetz des iterierten Logarithmus, Math. Ann., 101 (1929), 126–135 10.1007/BF01454828 MR1512520 CrossrefGoogle Scholar[2] J. Marcinkiewicz and , A. Zygmund, Remarque sur la loi du logarithme itéré, Fund. Math., 29 (1937), 215–222 0018.03204 Google Scholar[3] Mary Weiss, On the law of the iterated logarithm, J. Math. Mech., 8 (1959), 121–132 MR0102853 0091.14206 Google Scholar[4] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[5] V. V. Petrov, A bound for the deviation of the distribution of a sum of independent random variables from the normal law, Dokl. Akad. Nauk SSSR, 160 (1965), 1013–1015, (In Russian.) MR0178497 Google Scholar[6] V. V. Petrov, On the law of iterated logarithm, Vestnik Leningrad. Univ., 21 (1966), 63–67, (In Russian.) MR0212854 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Toward the History of the Saint Petersburg School of Probability and Statistics. I. Limit Theorems for Sums of Independent Random VariablesVestnik St. Petersburg University, Mathematics, Vol. 51, No. 2 | 16 June 2018 Cross Ref Limit Theorems in Hidden Markov ModelsIEEE Transactions on Information Theory, Vol. 59, No. 3 | 1 Mar 2013 Cross Ref Diamond aggregationMathematical Proceedings of the Cambridge Philosophical Society, Vol. 149, No. 2 | 10 May 2010 Cross Ref The characteristic polynomial of a random unitary matrix: A probabilistic approachDuke Mathematical Journal, Vol. 145, No. 1 | 1 Oct 2008 Cross Ref On the central limit theorem and the law of the iterated logarithmStatistics & Probability Letters, Vol. 78, No. 12 | 1 Sep 2008 Cross Ref On the Law of the Iterated Logarithm for a Sequence of Independent Random VariablesV. V. PetrovTheory of Probability & Its Applications, Vol. 46, No. 3 | 25 July 2006AbstractPDF (86 KB)The Borel-Cantelli lemma for strong mixing sequences of events and their applications to LILKodai Mathematical Journal, Vol. 2, No. 2 | 1 Jan 1979 Cross Ref On a strong law in information stability (Corresp.)IEEE Transactions on Information Theory, Vol. 23, No. 5 | 1 Sep 1977 Cross Ref A Theorem on the Law of the Iterated LogarithmV. V. PetrovTheory of Probability & Its Applications, Vol. 16, No. 4 | 17 July 2006AbstractPDF (223 KB)On the Law of the Iterated LogarithmV. A. EgorovTheory of Probability & Its Applications, Vol. 14, No. 4 | 17 July 2006AbstractPDF (577 KB) Volume 11, Issue 3| 1966Theory of Probability & Its Applications325-495 History Submitted:19 October 1965Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1111046Article page range:pp. 454-458ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics