Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 3, Pages 475–497
DOI: https://doi.org/10.4213/tvp3677
(Mi tvp3677)
 

This article is cited in 13 scientific papers (total in 13 papers)

A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III

G. P. Chistyakov

Institute for Low Temperature Physics and Engineering, Ukraine Academy of Sciences
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 of 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, 2003, Volume 47, Issue 3, Pages 395–414
DOI: https://doi.org/10.1137/S0040585X97979822
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. P. Chistyakov, “A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III”, Teor. Veroyatnost. i Primenen., 47:3 (2002), 475–497; Theory Probab. Appl., 47:3 (2003), 395–414
Citation in format AMSBIB
\Bibitem{Chi02}
\by G.~P.~Chistyakov
\paper A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem.~III
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 3
\pages 475--497
\mathnet{http://mi.mathnet.ru/tvp3677}
\crossref{https://doi.org/10.4213/tvp3677}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1975424}
\zmath{https://zbmath.org/?q=an:1034.60021}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 3
\pages 395--414
\crossref{https://doi.org/10.1137/S0040585X97979822}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000185370300002}
Linking options:
  • https://www.mathnet.ru/eng/tvp3677
  • https://doi.org/10.4213/tvp3677
  • https://www.mathnet.ru/eng/tvp/v47/i3/p475
    Cycle of papers
    This publication is cited in the following 13 articles:
    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
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024