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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 1, Pages 141–143 (Mi tvp573)  

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

Short Communications

On an estimate of the remainder in Lindeberg's theorem

I. A. Ibragimov, L. V. Osipov

Leningrad

Abstract: Let $X_1,X_2,…$ be a sequence of independent random variables which have the distribution functions $F_1(x),F_2(x),…$, the mean values $m_1,m_2,…$, the finite variances $\sigma_1^2,\sigma_2^2…$ and infinite absolute moments of order $2+\delta$ for any $\delta>0$. The examples of sequences are given for which the estimate
$$ \sup_x|F_n(x)-\Phi(x)|\le C\Psi_n(\varepsilon s_n) $$
does not hold true. Here $C$ is a constant, $\varepsilon$ is any fixed positive number and $F_n(x)$, $\Phi(x)$, $\Psi_n(\varepsilon s_n)$ are defined on p. 141.

Full text: PDF file (182 kB)

English version:
Theory of Probability and its Applications, 1966, 11:1, 125–128

Bibliographic databases:

Received: 03.07.1965

Citation: I. A. Ibragimov, L. V. Osipov, “On an estimate of the remainder in Lindeberg's theorem”, Teor. Veroyatnost. i Primenen., 11:1 (1966), 141–143; Theory Probab. Appl., 11:1 (1966), 125–128

Citation in format AMSBIB
\Bibitem{IbrOsi66}
\by I.~A.~Ibragimov, L.~V.~Osipov
\paper On an estimate of the remainder in Lindeberg's theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 1
\pages 141--143
\mathnet{http://mi.mathnet.ru/tvp573}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=196790}
\zmath{https://zbmath.org/?q=an:0203.19701}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 1
\pages 125--128
\crossref{https://doi.org/10.1137/1111008}


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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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. A. Ibragimov, E. L. Presman, Sh. K. Formanov, “O modifikatsiyakh uslovii Lindeberga i Rotarya v tsentralnoi predelnoi teoreme”, Teoriya veroyatn. i ee primen., 65:4 (2020), 818–822  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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