On Necessary and Sufficient Conditions for the Law of the Iterated Logarithm

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Previous article Next article On Necessary and Sufficient Conditions for the Law of the Iterated LogarithmA. I. Martikainen and V. V. PetrovA. I. Martikainen and V. V. Petrovhttps://doi.org/10.1137/1122002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. V. Petrov, Certain theorems of the type of the law of the iterated logarithm, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 41 (1974), 129–132, (In Russian.) MR0365673 Google Scholar[2] Leonard E. Baum, , M. Katz and , H. H. Stratton, Strong laws for ruled sums, Ann. Math. Statist., 42 (1971), 625–629 MR0290427 0217.21101 CrossrefGoogle Scholar[3] V. V. Petrov, On a generalization of a Levy inequality, Theory Prob. Applications, 20 (1975), 141–145 10.1137/1120012 0349.60001 LinkGoogle Scholar[4] V. V. Petrov, Sums of Independent Random Variables, Nauka, Moscow, 1972, (In Russian.) Google Scholar[5] Yu. V. Prohorov, On the strong law of large numbers, Izvestiya Akad. Nauk SSSR. Ser. Mat., 14 (1950), 523–536, (In Russian.) MR0038592 Google Scholar[6] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Spitzer Series and Regularly Varying FunctionsPseudo-Regularly Varying Functions and Generalized Renewal Processes | 13 October 2018 Cross Ref A Generalization of the Kolmogorov Theorem on the Law of the Iterated LogarithmTheory of Probability & Its Applications, Vol. 42, No. 1 | 17 February 2012AbstractPDF (121 KB)On the Strong Law of Large Numbers for Random Quadratic FormsTheory of Probability & Its Applications, Vol. 40, No. 1 | 28 July 2006AbstractPDF (1480 KB)Rates of convergence for tail seriesJournal of Statistical Planning and Inference, Vol. 43, No. 1-2 | 1 Jan 1995 Cross Ref On Strong Limit Theorems for Sums of Independent Random VariablesTheory of Probability & Its Applications, Vol. 37, No. 1 | 28 July 2006AbstractPDF (463 KB)On Convergence of Sums of Operator-Normed Independent Random VectorsTheory of Probability & Its Applications, Vol. 36, No. 2 | 17 July 2006AbstractPDF (568 KB)The Strong Law of Large Numbers for Sums of Independent Random Vectors with Operator Normalizations and Null Convergence of Gaussian SequencesTheory of Probability & Its Applications, Vol. 32, No. 2 | 17 July 2006AbstractPDF (1225 KB)The Contraction Principle and the Strong Law of Large Numbers for Weighted SumsTheory of Probability & Its Applications, Vol. 31, No. 3 | 28 July 2006AbstractPDF (1191 KB)On the One-Sided Law of the Iterated LogarithmTheory of Probability & Its Applications, Vol. 30, No. 4 | 28 July 2006AbstractPDF (910 KB)Summary of Reports Presented at Sessions of the Seminar in Probability Theory and Mathematical Statistics at the Shevchenko State University, KievTheory of Probability & Its Applications, Vol. 30, No. 3 | 17 July 2006AbstractPDF (1098 KB)Criteria for Strong Convergence of Normalized Sums of Independent Random Variables and Their ApplicationsTheory of Probability & Its Applications, Vol. 29, No. 3 | 17 July 2006AbstractPDF (1300 KB)One-Sided Versions of Strong Limit TheoremsTheory of Probability & Its Applications, Vol. 28, No. 1 | 17 July 2006AbstractPDF (1252 KB)On the limiting behavior of normed sums of independent random variablesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 68, No. 1 | 1 Jan 1984 Cross Ref On the Convergence Rate in the Strong Law of Large NumbersTheory of Probability & Its Applications, Vol. 26, No. 1 | 17 July 2006AbstractPDF (486 KB)On the law of the iterated logarithm in the infinite variance caseJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 30, No. 1 | 9 April 2009 Cross Ref On Necessary and Sufficient Conditions for the Strong Law of Large NumbersTheory of Probability & Its Applications, Vol. 24, No. 4 | 17 July 2006AbstractPDF (726 KB) Volume 22, Issue 1| 1977Theory of Probability & Its Applications1-202 History Submitted:16 December 1975Published online:17 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1122002Article page range:pp. 16-23ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics