On the Accuracy of Normal Approximation of the Probability of Hitting a Ball

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Previous article Next article On the Accuracy of Normal Approximation of the Probability of Hitting a BallV. V. YurinskiiV. V. Yurinskiihttps://doi.org/10.1137/1127030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. I. Chebotarev, Estimates of the convergence rate in the central limit theorem in $l\sb{p}$, Sibirsk. Mat. Zh., 20 (1979), 1099–1116, 1167, (In Russian.) 81e:60005 Google Scholar[2] F. Götze, Asymptotic expansions for bivariate von Mises functionals, Z. Wahrsch. Verw. Gebiete, 50 (1979), 333–355 81c:60025 0405.60009 CrossrefGoogle Scholar[3] Yu. Borovskikh and , A. Rackauskas, Asymptotic behavior of distributions in Banach spaces, Litovsk. Mat. Sb., 19 (1979), 39–54, 209 81c:60007 0441.60009 Google Scholar[4] J. Kuelbs and , T. Kurtz, Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm, Ann. Probability, 2 (1974), 387–407 50:14868 0298.60017 CrossrefGoogle Scholar[5] I. I. 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Probab., 14 (1986), 922–942 87i:60013 0599.60009 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Explicit rates of approximation in the CLT for quadratic formsThe Annals of Probability, Vol. 42, No. 1 Cross Ref Some Approximation Problems in Statistics and Probability9 March 2013 Cross Ref Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert spaceJournal of Multivariate Analysis, Vol. 97, No. 9 Cross Ref Berry–Esseen inequality for linear processes in Hilbert spacesStatistics & Probability Letters, Vol. 63, No. 3 Cross Ref Lattice points in multidimensional bodiesForum Mathematicum, Vol. 13, No. 2 Cross Ref Optimal Bounds in Non-Gaussian Limit Theorems for U-StatisticsThe Annals of Probability, Vol. 27, No. 1 Cross Ref On the Accuracy of Normal Approximation of the Probability of Hitting a Ball of Sums of Weakly Dependent Hilbert Space Valued Random Variables IIA. N. 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