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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 2, Pages 339–342 (Mi tvp630)  

This article is cited in 10 scientific papers (total in 10 papers)

Short Communications

Refinement of Lindeberg's theorem

L. V. Osipov

Leningrad

Abstract: An estimate is given for the remainder in the central limit theorem for the sums of independent non-identically distributed random variables. The main result (theorem 1) is a generalization of the known results by Liapounoff and Esseen.

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English version:
Theory of Probability and its Applications, 1966, 11:2, 299–302

Bibliographic databases:

Received: 22.03.1965

Citation: L. V. Osipov, “Refinement of Lindeberg's theorem”, Teor. Veroyatnost. i Primenen., 11:2 (1966), 339–342; Theory Probab. Appl., 11:2 (1966), 299–302

Citation in format AMSBIB
\Bibitem{Osi66}
\by L.~V.~Osipov
\paper Refinement of Lindeberg's theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 2
\pages 339--342
\mathnet{http://mi.mathnet.ru/tvp630}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=205312}
\zmath{https://zbmath.org/?q=an:0147.37001}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 2
\pages 299--302
\crossref{https://doi.org/10.1137/1111026}


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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. V. Yu. Korolev, I. G. Shevtsova, “On the accuracy of the normal approximation. II”, Theory Probab. Appl., 50:3 (2006), 473–482  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. Yu. Korolev, S. Popov, “An improvement of the convergence rate estimates in the central limit theorem when moments of order greater than two are absent”, Theory Probab. Appl., 56:4 (2011), 682–691  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. Yu. S. Nefedova, I. G. Shevtsova, “Nonuniform estimates of convergence rate in the central limit theorem”, Theory Probab. Appl., 57:1 (2013), 28–59  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Korolev V.Yu. Popov S.V., “Improvement of Convergence Rate Estimates in the Central Limit Theorem Under Weakened Moment Conditions”, Dokl. Math., 86:1 (2012), 506–511  crossref  isi
    5. Korolev V.Yu., Popov S.V., “Utochnenie otsenok skorosti skhodimosti v tsentralnoi predelnoi teoreme pri oslablennykh momentnykh usloviyakh”, Doklady akademii nauk, 445:3 (2012), 265–265  elib
    6. V. Yu. Korolev, A. V. Dorofeyeva, “Estimates for the concentration functions under the weakened moments”, Theory Probab. Appl., 62:1 (2018), 84–97  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Korolev V. Dorofeeva A., “Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions?”, Lith. Math. J., 57:1 (2017), 38–58  crossref  mathscinet  isi  scopus
    8. Shevtsova I., “On the Absolute Constants in Nagaev-Bikelis-Type Inequalities”, Inequalities and Extremal Problems in Probability and Statistics: Selected Topics, ed. Pinelis I., Academic Press Ltd-Elsevier Science Ltd, 2017, 47–102  crossref  isi
    9. M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    10. V. Yu. Korolev, A. V. Dorofeeva, “O neravnomernykh otsenkakh tochnosti normalnoi approksimatsii dlya raspredelenii nekotorykh sluchainykh summ pri oslablennykh momentnykh usloviyakh”, Inform. i ee primen., 12:4 (2018), 86–91  mathnet  crossref  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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