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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
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
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
Linking options:
https://www.mathnet.ru/eng/tvp11https://doi.org/10.4213/tvp11 https://www.mathnet.ru/eng/tvp/v52/i1/p173
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Abstract page: | 410 | Full-text PDF : | 190 | References: | 52 | First page: | 22 |
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