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• W1974790354 abstract "Next article Two-Dimensional Analogues of an Inequality of Esseen with Applications to the Central Limit TheoremS. M. SadikovaS. M. Sadikovahttps://doi.org/10.1137/1111035PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Carl-Gustav Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math., 77 (1945), 1–125 MR0014626 0060.28705 CrossrefGoogle Scholar[2] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 MR0062975 0056.36001 Google Scholar[3] Harald Bergström, On the central limit theorem in the space $Rsb k, k>1$, Skand. Aktuarietidskr., 28 (1945), 106–127 MR0015704 0060.28708 Google Scholar[4] Harald Bergström, On the central limit theorem in the case of not equally distributed random variables, Skand. Aktuarietidskr., 32 (1949), 37–62 MR0032113 0041.45202 Google Scholar[5] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[6] S. M. Sadikova, Some inequalities for characteristic functions, Theor. Prob. Applications, 11 (1966), , this issue. (English Translation.) LinkGoogle Scholar[7] C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2), 75 (1962), 81–92 MR0142978 0111.34803 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Smooth bootstrapping of copula functionalsElectronic Journal of Statistics, Vol. 16, No. 1 | 1 Jan 2022 Cross Ref Normal limit law for protected node profile of random recursive treesТеория вероятностей и ее применения, Vol. 67, No. 3 | 22 July 2022 Cross Ref On some inequalities for ψ -mixing sequences and its applications in conditional value-at-risk estimateCommunications in Statistics - Theory and Methods, Vol. 49, No. 22 | 22 May 2019 Cross Ref On the bivariate Erdős–Kac theorem and correlations of the Möbius functionMathematical Proceedings of the Cambridge Philosophical Society, Vol. 169, No. 3 | 14 August 2019 Cross Ref MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOSForum of Mathematics, Pi, Vol. 8 | 20 January 2020 Cross Ref Stability of Characterization of the Independence of Random Variables by the Independence of Linear StatisticsD. 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SadikovaTheory of Probability & Its Applications, Vol. 13, No. 1 | 17 July 2006AbstractPDF (534 KB)Some Inequalities for Characteristic FunctionsS. M. SadikovaTheory of Probability & Its Applications, Vol. 11, No. 3 | 17 July 2006AbstractPDF (506 KB) Volume 11, Issue 3| 1966Theory of Probability & Its Applications325-495 History Submitted:25 May 1966Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1111035Article page range:pp. 325-335ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics" @default.
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