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Teor. Veroyatnost. i Primenen., 1978, Volume 23, Issue 2, Pages 376–379 (Mi tvp3043)  

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

Short Communications

A sharpened form of the inequality for the concentration function

L. P. Postnikova, A. A. Yudin

Moscow

Abstract: By means of the additive number theory the following sharpened form of Kesten's theorem for the concentration function is obtained.
Let $X_1,…,X_n$ be independent random variables,
$$ S_n=X_1+…+X_n, Q(X,\lambda)=\sup_x\mathbf P(x\le X\le x+\lambda). $$
Let $\lambda_j$, $1\le j\le n$, be any positive numbers such that $\lambda_j\ge 2\lambda$. Then
$$ Q(S_n,\lambda)\ll4\lambda[\sum_{j=1}^n\lambda_j^2(1-Q(X_j,\lambda_j))Q^{-2}(X_j,\lambda)]^{-1/2}. $$


Full text: PDF file (206 kB)

English version:
Theory of Probability and its Applications, 1979, 23:2, 359–362

Bibliographic databases:

Received: 30.03.1977

Citation: L. P. Postnikova, A. A. Yudin, “A sharpened form of the inequality for the concentration function”, Teor. Veroyatnost. i Primenen., 23:2 (1978), 376–379; Theory Probab. Appl., 23:2 (1979), 359–362

Citation in format AMSBIB
\Bibitem{PosYud78}
\by L.~P.~Postnikova, A.~A.~Yudin
\paper A~sharpened form of the inequality for the concentration function
\jour Teor. Veroyatnost. i Primenen.
\yr 1978
\vol 23
\issue 2
\pages 376--379
\mathnet{http://mi.mathnet.ru/tvp3043}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=517929}
\zmath{https://zbmath.org/?q=an:0421.60048|0388.60049}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 23
\issue 2
\pages 359--362
\crossref{https://doi.org/10.1137/1123037}


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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. Gotze F., Zaitsev A.Y., “A multiplicative inequality for concentration functions of n-fold convolutions”, High Dimensional Probability II, Progress in Probability, 47, 2000, 39–47  isi
    2. S. G. Bobkov, G. P. Chistyakov, “Bounds on the maximum of the density for sums of independent random variables”, J. Math. Sci. (N. Y.), 199:2 (2014), 100–106  mathnet  crossref  mathscinet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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