On the Strong Law of Large Numbers and the Law of the Iterated Logarithm for Sequences of Independent Random Variables

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Previous article Next article On the Strong Law of Large Numbers and the Law of the Iterated Logarithm for Sequences of Independent Random VariablesV. A. EgorovV. A. Egorovhttps://doi.org/10.1137/1115053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Henry Teicher, Some new conditions for the strong law, Proc. Nat. Acad. Sci. U.S.A., 59 (1968), 705–707 MR0222940 0211.49103 CrossrefGoogle Scholar[2] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[3] William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons Inc., New York, 1968xviii+509 MR0228020 0155.23101 Google Scholar[4] G. M. Fikhtengol'ts, A Course in Differential and Integral Calculus, Vol. 2, Izd-vo, “Nauka”, Moscow, 1966 Google Scholar[5] A. Kolmogoroff, Über das Gesetz des iterierten Logarithmus, Math. Ann., 101 (1929), 126–135 10.1007/BF01454828 MR1512520 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails de La Vallée Poussin’s theorem, uniform integrability, tightness and momentsStatistics & Probability Letters, Vol. 107 | 1 Dec 2015 Cross Ref Comparing sums of independent bounded random variables and sums of Bernoulli random variablesStatistics & Probability Letters, Vol. 34, No. 3 | 1 Jun 1997 Cross Ref Limit Theorems for Independent Random VariablesProbability Theory | 1 Jan 1997 Cross Ref On the Strong Law of Large Numbers and the Law of the Iterated Logarithm for Martingales and Sums of Independent Random VariablesV. A. EgorovTheory of Probability & Its Applications, Vol. 35, No. 4 | 17 July 2006AbstractPDF (1294 KB)Limit Theorems for Independent Random VariablesProbability Theory | 1 Jan 1988 Cross Ref Sufficient moment and truncated moment conditions for the law of the iterated logarithmProbability Theory and Related Fields, Vol. 75, No. 4 | 1 Aug 1987 Cross Ref A Way of Proving Theorems on the Law of the Iterated LogarithmV. A. EgorovTheory of Probability & Its Applications, Vol. 29, No. 1 | 17 July 2006AbstractPDF (603 KB)Criteria for Strong Convergence of Normalized Sums of Independent Random Variables and Their ApplicationsA. I. MartikainenTheory of Probability & Its Applications, Vol. 29, No. 3 | 17 July 2006AbstractPDF (1300 KB)Relative stability of trimmed sumsZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 66, No. 1 | 1 Jan 1984 Cross Ref 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 Lindeberg functions and the law of the iterated logarithmZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 65, No. 1 | 1 Jan 1983 Cross Ref On the Distribution of Sums of Independent Random Variables with Values in a Banach SpaceI. F. PinelisTheory of Probability & Its Applications, Vol. 23, No. 3 | 17 July 2006AbstractPDF (691 KB)Generalized exponential bounds, iterated logarithm and strong lawsZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 48, No. 3 | 1 Jan 1979 Cross Ref Some Inequalities for the Distribution of Sums of Independent Random VariablesS. V. Nagaev and I. F. PinelisTheory of Probability & Its Applications, Vol. 22, No. 2 | 17 July 2006AbstractPDF (687 KB)Limit Theorems for Independent Random VariablesProbability Theory | 1 Jan 1978 Cross Ref On the Strong Law of Large NumbersS. V. Nagaev and N. A. VolodinTheory of Probability & Its Applications, Vol. 20, No. 3 | 17 July 2006AbstractPDF (402 KB)A necessary condition for the iterated logarithm lawZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 31, No. 4 | 1 Jan 1975 Cross Ref Some Theorems on the Strong Law of Large Numbers and Law of the Iterated LogarithmV. A. EgorovTheory of Probability & Its Applications, Vol. 17, No. 1 | 17 July 2006AbstractPDF (1139 KB)Probability Inequalities for Sums of Independent Random VariablesD. Kh. Fuk and S. V. NagaevTheory of Probability & Its Applications, Vol. 16, No. 4 | 17 July 2006AbstractPDF (1115 KB) Volume 15, Issue 3| 1970Theory of Probability & Its Applications359-556 History Submitted:06 July 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115053Article page range:pp. 509-514ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics