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Teor. Veroyatnost. i Primenen., 1996, Volume 41, Issue 3, Pages 561–577 (Mi tvp3137)  

This article is cited in 5 scientific papers (total in 5 papers)

An estimate of the concentration function by the Esseen method

N. P. Salikhov

Essential Administration of Information Systems

Abstract: The paper deals with the Esseen method of obtaining upper estimates for the concentration function of a random variable $X$ in terms of the characteristic function of $X$. Some problems of the parametric optimization of such estimates are solved. Applications are described to the estimation of the probabilities of large deviations of the sums of identically distributed random variables.

Keywords: concentration function, characteristic function, probabilities of large deviations, Poisson summation formula, Esseen inequality, Euler numbers.

DOI: https://doi.org/10.4213/tvp3137

Full text: PDF file (779 kB)

English version:
Theory of Probability and its Applications, 1997, 41:3, 504–518

Bibliographic databases:

Received: 02.08.1993

Citation: N. P. Salikhov, “An estimate of the concentration function by the Esseen method”, Teor. Veroyatnost. i Primenen., 41:3 (1996), 561–577; Theory Probab. Appl., 41:3 (1997), 504–518

Citation in format AMSBIB
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\by N.~P.~Salikhov
\paper An estimate of the concentration function by the Esseen method
\jour Teor. Veroyatnost. i Primenen.
\yr 1996
\vol 41
\issue 3
\pages 561--577
\mathnet{http://mi.mathnet.ru/tvp3137}
\crossref{https://doi.org/10.4213/tvp3137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1450074}
\zmath{https://zbmath.org/?q=an:0883.60020}
\transl
\jour Theory Probab. Appl.
\yr 1997
\vol 41
\issue 3
\pages 504--518
\crossref{https://doi.org/10.1137/S0040585X9797523X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997XZ71800007}


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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. Roos B., “On Hipp's compound Poisson approximations via concentration functions”, Bernoulli, 11:3 (2005), 533–557  crossref  mathscinet  zmath  isi  elib  scopus
    2. Theory Probab. Appl., 52:1 (2008), 148–152  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Adell J.A., Lekuona A., “Berry–Esseen bounds for standardized subordinators via moduli of smoothness”, Journal of Theoretical Probability, 20:2 (2007), 221–235  crossref  mathscinet  zmath  isi  scopus
    4. Siegmund-Schultze R., von Weizsaecker H., “Level crossing probabilities II: Polygonal recurrence of multidimensional random walks”, Advances in Mathematics, 208:2 (2007), 680–698  crossref  mathscinet  zmath  isi  scopus
    5. Tao T., Vu V.H., “Inverse Littlewood–Offord theorems and the condition number of random discrete matrices”, Annals of Mathematics, 169:2 (2009), 595–632  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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