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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 2, Pages 326–344
DOI: https://doi.org/10.4213/tvp3921 (Mi tvp3921) 		 
This article is cited in 21 scientific papers (total in 21 papers)

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

G. P. Chistyakov

Institute for Low Temperature Physics and Engineering, Ukraine Academy of Sciences
Full-text PDF (1701 kB) Citations (21)
DOI: https://doi.org/10.4213/tvp3921
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 necessarily 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 2, Pages 226–242
DOI: https://doi.org/10.1137/S0040585X97978932
Bibliographic databases:
Language: Russian
Citation: G. P. Chistyakov, “A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. I.”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 326–344; Theory Probab. Appl., 46:2 (2002), 226–242
Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 2
\pages 226--242
\crossref{https://doi.org/10.1137/S0040585X97978932}
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  • https://www.mathnet.ru/eng/tvp3921
  • https://doi.org/10.4213/tvp3921
  • https://www.mathnet.ru/eng/tvp/v46/i2/p326
    Cycle of papers
    This publication is cited in the following 21 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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