S. M. Sadikova, “On the multidimensional central limit theorem”, Teor. Veroyatnost. i Primenen., 13:1 (1968), 164–170; Theory Probab. Appl., 13:1 (1968), 164

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Teoriya Veroyatnostei i ee Primeneniya, 1968, Volume 13, Issue 1, Pages 164–170 (Mi tvp830)

This article is cited in 11 scientific papers (total in 11 papers)

Short Communications

On the multidimensional central limit theorem

S. M. Sadikova

Moscow Engineering Physics Institute

Full-text PDF (1048 kB) Citations (11)

Abstract: Two estimations in the central limit theorem for equally distributed random vectors in

$R^s$ are given. The first one involves distribution functions (for

$s=2$ ) and is an improvement of previous results stated in [1] and [2]. The second one concerns (for arbitrary

$s$ ) “the distance”

$\rho_2$ defined as

$\sup_A|P(A)-Q(A)|$
where the supremum is taken over all measurable convex sets

$A\in R^s$ (cf. [5]).

Received: 23.05.1967

English version:
Theory of Probability and its Applications, 1968, Volume 13, Issue 1, Pages 164–170
DOI: https://doi.org/10.1137/1113015

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: S. M. Sadikova, “On the multidimensional central limit theorem”, Teor. Veroyatnost. i Primenen., 13:1 (1968), 164–170; Theory Probab. Appl., 13:1 (1968), 164–170

Citation in format AMSBIB

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\by S.~M.~Sadikova

\paper On the multidimensional central limit theorem

\jour Teor. Veroyatnost. i Primenen.

\yr 1968

\vol 13

\issue 1

\pages 164--170

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=226714}

\zmath{https://zbmath.org/?q=an:0196.20503}

\transl

\jour Theory Probab. Appl.

\yr 1968

\vol 13

\issue 1

\pages 164--170

\crossref{https://doi.org/10.1137/1113015}

Linking options:

https://www.mathnet.ru/eng/tvp830

https://www.mathnet.ru/eng/tvp/v13/i1/p164

This publication is cited in the following 11 articles:

F. G. Gabbasov, V. T. Dubrovin, M. S. Fadeeva, “On the estimation of the convergence rate in the multidimentional limit theorem for the sum of weakly dependent random variables functions”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 266–274
Peter Hall, Rabi N. Bhattacharya, 2016, 3
V. T. Dubrovin, F. G. Gabbasov, V. Ju. Chebakova, “Multidimensional central limit theorem for sums of functions of the trajectories of endomorphisms”, Lobachevskii J Math, 37:4 (2016), 409
F. G. Gabbasov, V. T. Dubrovin, V. S. Kugurakov, “O mnogomernoi predelnoi teoreme dlya endomorfizmov evklidova prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2015, 25–34
F. G. Gabbasov, V. T. Dubrovin, “Mnogomernaya predelnaya teorema o bolshikh ukloneniyakh dlya endomorfizmov evklidova prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 156, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2014, 16–24
F. G. Gabbasov, V. T. Dubrovin, “Otsenka skorosti skhodimosti v mnogomernoi predelnoi teoreme dlya endomorfizmov evklidova prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2013, 33–43
R. M. Gil'fanov, “A nonuniform estimate of the rate of convergence in the central limit theorem for the sum of vector-valued functions of independent variables”, Theory Probab. Appl., 26:4 (1982), 773–786
F. G. Gabbasov, V. T. Dubrovin, “Probability that the normed sum of weakly dependent vectors falls in the exterior of a convex set”, J. Soviet Math., 43:1 (1988), 2187–2193
F. G. Gabbasov, “A multidimensional central limit theorem for sums of functions of sequences with mixing”, Lith Math J, 17:4 (1978), 494
V. I. Rotar', “Nonclassical estimates of the rate of convergence in the multidimensional central limit theorem. I”, Theory Probab. Appl., 22:4 (1978), 755–772
V. I. Rotar', “A nonuniform estimate of the speed of convergence in the multidimensional central limit theorem”, Theory Probab. Appl., 15:4 (1970), 630–648

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

Theory of Probability and its Applications

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