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Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 4, Pages 738–742 (Mi tvp931)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On the problem of the stability of the decomposition of the normal law into components

V. M. Zolotarev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: The following theorem is proved: Let $\Phi$ be the distribution function of $N(0,1)$, $L$ the Levy metric and $F=F_1*F_2$ a distribution function such that
$$ L(F,\Phi)\le\varepsilon<1. $$
Then, there can be found a normal distribution $\Phi_1$ such that
$$ C_1(\log\frac1\varepsilon)^{-1/2}<L(F_1,\Phi_1)<C_2(\log\frac1\varepsilon)^{-1/11}, $$
where $C_1$ and $C_2$ are positive constants.

Full text: PDF file (306 kB)

English version:
Theory of Probability and its Applications, 1968, 13:4, 697–700

Bibliographic databases:

Received: 12.03.1968

Citation: V. M. Zolotarev, “On the problem of the stability of the decomposition of the normal law into components”, Teor. Veroyatnost. i Primenen., 13:4 (1968), 738–742; Theory Probab. Appl., 13:4 (1968), 697–700

Citation in format AMSBIB
\Bibitem{Zol68}
\by V.~M.~Zolotarev
\paper On the problem of the stability of the decomposition of the normal law into components
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 4
\pages 738--742
\mathnet{http://mi.mathnet.ru/tvp931}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=240852}
\zmath{https://zbmath.org/?q=an:0181.46002|0176.49101}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 4
\pages 697--700
\crossref{https://doi.org/10.1137/1113087}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Theory Probab. Appl., 57:4 (2013), 568–588  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Bobkov S.G. Chistyakov G.P. Goetze F., “Regularized distributions and entropic stability of Cramer's characterization of the normal law”, Stoch. Process. Their Appl., 126:12, SI (2016), 3865–3887  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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