Bounds for the Convergence Rate of Numerical Characteristics in Limit Theorems with Stable Limit Law

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Previous article Next article Bounds for the Convergence Rate of Numerical Characteristics in Limit Theorems with Stable Limit LawA. I. DaugavetA. I. Daugavethttps://doi.org/10.1137/1132079PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. I. Daugavet, Convergence of certain numerical characteristics of sums of independent random variables to the corresponding characteristics of stable laws, Deposited with the VINITI, No. 1681–1684. (In Russian.) Google Scholar[2] V. M. Kruglov, Convergence of numerical characteristics of sums of independent random variables with values in Hilbert space, Theory Probab. Appl., 18 (1973), 694–712 10.1137/1118091 0321.60045 LinkGoogle Scholar[3] V. I. Paulauskas, Estimates of the remainder term in limit theorems in the case of stable limit law, Lithuanian Math. J., 14 (1974), 127–146 0306.60012 CrossrefGoogle Scholar[4] V. I. Paulauskas, Uniform and nonuniform estimates of the remainder term in a limit theorem with a stable limit law, Lithuanian Math J., 14 (1974), 661–672 0334.60014 CrossrefGoogle Scholar[5] S. Steishunas, On the nonuniform convergence rate to a stable limit law, Summaries of Reports of the 24th Conference of the Lithuanian Mathematical Society (Vilnius, June 22–23, 1983), Inst. Math. and Cybern. Lith. Acad. Sci, Vilnius, 1983, 184–185, (In Russian.) Google Scholar[6] P. L. Butzer and , L. Hahn, General theorems on rates of convergence in distribution of random variables. II. Applications to the stable limit laws and weak law of large numbers, J. Multivariate Anal., 8 (1978), 202–221 10.1016/0047-259X(78)90072-6 80a:60026b 0383.60025 CrossrefGoogle Scholar[7] Michael J. Klass, A method of approximating expectations of functions of sums of independent random variables, Ann. Probab., 9 (1981), 413–428 82f:60119 0463.60023 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 32, Issue 3| 1988Theory of Probability & Its Applications History Submitted:22 October 1985Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1132079Article page range:pp. 531-535ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics