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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 3, Pages 573–579
DOI: https://doi.org/10.4213/tvp3905 (Mi tvp3905) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Short Communications

A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. II

G. P. Chistyakov

Institute for Low Temperature Physics and Engineering, Ukraine Academy of Sciences
Full-text PDF (643 kB) Citations (13)
DOI: https://doi.org/10.4213/tvp3905
Abstract: A new asymptotic expansion is obtained in Lyapunov's central limit theorem for distribution functions of centered and normed sums of independent random variables which are not necessary identically distributed. It is applied to determine the asymptotically best constants in the Berry–Esseen inequality, thus solving problems about their optimal values raised by Kolmogorov and Zolotarev.
Keywords: central limit theorem, Lyapunov's theorem, Berry–Esseen bounds, asymptotic expansion, characteristic functions.
Received: 30.06.1998
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 3, Pages 516–522
DOI: https://doi.org/10.1137/S0040585X97979172
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. P. Chistyakov, “A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. II”, Teor. Veroyatnost. i Primenen., 46:3 (2001), 573–579; Theory Probab. Appl., 46:3 (2002), 516–522
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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  • https://doi.org/10.4213/tvp3905
  • https://www.mathnet.ru/eng/tvp/v46/i3/p573
    Cycle of papers
    This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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