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Mat. Zametki, 1975, Volume 18, Issue 1, Pages 129–135 (Mi mz7634)  

This article is cited in 4 scientific papers (total in 5 papers)

An extension of the Lindeberg–Feller theorem

V. I. Rotar'

Central Economics and Mathematics Institute, Academy of Sciences of the USSR

Abstract: A new version is presented of the necessary and sufficient condition of convergence, to a normal law, of sums of independent variables in a nonclassical situation (i.e., absence of limiting negligibility of variables). The obtained condition differs from previously obtained conditions by the fact that it does not use Levy's metric and that is is closer to classical formulations. A similar condition is sufficient for the closeness of two convolutions when the number of components of the convolutions increases without bounds.

Full text: PDF file (425 kB)

English version:
Mathematical Notes, 1975, 18:1, 660–663

Bibliographic databases:

UDC: 519.21.9
Received: 10.11.1974

Citation: V. I. Rotar', “An extension of the Lindeberg–Feller theorem”, Mat. Zametki, 18:1 (1975), 129–135; Math. Notes, 18:1 (1975), 660–663

Citation in format AMSBIB
\Bibitem{Rot75}
\by V.~I.~Rotar'
\paper An extension of the Lindeberg--Feller theorem
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 129--135
\mathnet{http://mi.mathnet.ru/mz7634}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=400348}
\zmath{https://zbmath.org/?q=an:0348.60025}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 660--663
\crossref{https://doi.org/10.1007/BF01461150}


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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. Sh. K. Formanov, “The Stein–Tikhomirov Method and a Nonclassical Central Limit Theorem”, Math. Notes, 71:4 (2002), 550–555  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Sh. K. Formanov, “On the Stein–Tikhomirov method and its applications in nonclassical limit theorems”, Discrete Math. Appl., 17:1 (2007), 23–36  mathnet  crossref  crossref  mathscinet  zmath  elib
    4. “Abstracts of Talks Given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172  mathnet  crossref  crossref  isi  elib
    5. 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
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