An Estimate for the Remainder Term in the Central Limit Theorem for Sums of Functions of Independent Variables and Sums of the Form $\sum {f(t2^k )} $

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Previous article Next article An Estimate for the Remainder Term in the Central Limit Theorem for Sums of Functions of Independent Variables and Sums of the Form $\sum {f(t2^k )} $V. I. Ladokhin and D. A. MoskvinV. I. Ladokhin and D. A. Moskvinhttps://doi.org/10.1137/1116008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. V. Nagaev, Some limit theorems for large deviations, Theory Prob. Applications, 10 (1965), 214–235 10.1137/1110027 0144.18704 LinkGoogle Scholar[2] A. Bikjalis, Estimates of the remainder term in the central limit theorem, Litovsk. Mat. Sb., 6 (1966), 323–346, (In Russian.) MR0210173 Google Scholar[3] I. A. Ibragimov, The central limit theorem for sums of functions of independent variables and sums of the form $\Sigma f(t2^{k})$, Theory Prob. Applications, 12 (1967), 596–607 10.1137/1112075 0217.49803 LinkGoogle Scholar[4] I. A. Ibragimov and , Yu. V. Linnik, Independent and Stationarily Related Variables, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Berry–Esseen theorems under weak dependenceThe Annals of Probability, Vol. 44, No. 3 Cross Ref A Non-Uniform Estimate of the Rate of Convergence in the Central Limit Theorem for the Sums of Vector-Valued Functions of Independent VariablesR. M. Gil’fanov17 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 4AbstractPDF (830 KB)The Central Limit Theorem for Sums of Functions of Mixing SequencesV. T. Dubrovin and D. A. Moskvin17 July 2006 | Theory of Probability & Its Applications, Vol. 24, No. 3AbstractPDF (701 KB)A Local Limit Theorem for the Distribution of Fractional Parts of an Exponential FunctionD. A. Moskvin and A. G. Postnikov17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 3AbstractPDF (548 KB) Volume 16, Issue 1| 1971Theory of Probability & Its Applications History Submitted:19 March 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1116008Article page range:pp. 116-125ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics