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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1970, Volume 15, Issue 4, Pages 647–665 (Mi tvp1932)

A nonuniform estimate of the speed of convergence in the multidimensional central limit theorem

V. I. Rotar'

Moscow

Abstract: In the paper, by the method of characteristic functions, an estimate of the convergence rate in the multi-dimensional central limit theorem is obtained. The estimate is non-uniform; it depends on the location with respect to the origin of the set the measures of which are compaired.

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English version:
Theory of Probability and its Applications, 1970, 15:4, 630–648

Bibliographic databases:

Citation: V. I. Rotar', “A nonuniform estimate of the speed of convergence in the multidimensional central limit theorem”, Teor. Veroyatnost. i Primenen., 15:4 (1970), 647–665; Theory Probab. Appl., 15:4 (1970), 630–648

Citation in format AMSBIB
\Bibitem{Rot70} \by V.~I.~Rotar' \paper A~nonuniform estimate of the speed of convergence in the multidimensional central limit theorem \jour Teor. Veroyatnost. i Primenen. \yr 1970 \vol 15 \issue 4 \pages 647--665 \mathnet{http://mi.mathnet.ru/tvp1932} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=283858} \zmath{https://zbmath.org/?q=an:0235.60026} \transl \jour Theory Probab. Appl. \yr 1970 \vol 15 \issue 4 \pages 630--648 \crossref{https://doi.org/10.1137/1115072} 

• http://mi.mathnet.ru/eng/tvp1932
• http://mi.mathnet.ru/eng/tvp/v15/i4/p647

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 151–175
2. V. A. Koval', “The Law of the Iterated Logarithm for Matrix-Normed Sums of Independent Random Variables and Its Applications”, Math. Notes, 72:3 (2002), 331–336
3. P. G. Grigor'ev, “Random Linear Combinations of Functions from $L_1$”, Math. Notes, 74:2 (2003), 185–211
4. Bogatyrev S.A., Goetze F., Ulyanov V.V., “Non–uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space”, Journal of Multivariate Analysis, 97:9 (2006), 2041–2056
5. Theory Probab. Appl., 52:4 (2008), 636–650