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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
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DOI: https://doi.org/10.4213/tvp11
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
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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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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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