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Teoriya Veroyatnostei i ee Primeneniya, 2007, Volume 52, Issue 1, Pages 173–175
DOI: https://doi.org/10.4213/tvp11
(Mi tvp11)
 

Short Communications

On the necessity of the Lyapunov condition for normal convergence

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
References:
Abstract: This paper provides necessary and sufficient conditions for the weak convergence of the distributions of sums of independent random variables to the normal distribution. The conditions are given as a combination of a part of the assumption of the classic criterion for the normal convergence and the Lyapunov condition for truncated random variables.
Keywords: normal convergence, Lindeberg–Feller theorem, weak convergence, Lyapunov condition.
Received: 04.05.2005
English version:
Theory of Probability and its Applications, 2008, Volume 52, Issue 1, Pages 164–166
DOI: https://doi.org/10.1137/S0040585X97982888
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Kruglov, “On the necessity of the Lyapunov condition for normal convergence”, Teor. Veroyatnost. i Primenen., 52:1 (2007), 173–175; Theory Probab. Appl., 52:1 (2008), 164–166
Citation in format AMSBIB
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  • https://doi.org/10.4213/tvp11
  • https://www.mathnet.ru/eng/tvp/v52/i1/p173
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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    References:52
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