RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1975, Volume 18, Issue 1, Pages 129–135 (Mi mz7634)

An extension of the Lindeberg–Feller theorem

V. I. Rotar'

Central Economics and Mathematics Institute, Academy of Sciences of the USSR

Abstract: A new version is presented of the necessary and sufficient condition of convergence, to a normal law, of sums of independent variables in a nonclassical situation (i.e., absence of limiting negligibility of variables). The obtained condition differs from previously obtained conditions by the fact that it does not use Levy's metric and that is is closer to classical formulations. A similar condition is sufficient for the closeness of two convolutions when the number of components of the convolutions increases without bounds.

Full text: PDF file (425 kB)

English version:
Mathematical Notes, 1975, 18:1, 660–663

Bibliographic databases:

UDC: 519.21.9

Citation: V. I. Rotar', “An extension of the Lindeberg–Feller theorem”, Mat. Zametki, 18:1 (1975), 129–135; Math. Notes, 18:1 (1975), 660–663

Citation in format AMSBIB
\Bibitem{Rot75} \by V.~I.~Rotar' \paper An extension of the Lindeberg--Feller theorem \jour Mat. Zametki \yr 1975 \vol 18 \issue 1 \pages 129--135 \mathnet{http://mi.mathnet.ru/mz7634} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=400348} \zmath{https://zbmath.org/?q=an:0348.60025} \transl \jour Math. Notes \yr 1975 \vol 18 \issue 1 \pages 660--663 \crossref{https://doi.org/10.1007/BF01461150} 

• http://mi.mathnet.ru/eng/mz7634
• http://mi.mathnet.ru/eng/mz/v18/i1/p129

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 151–175
2. Sh. K. Formanov, “The Stein–Tikhomirov Method and a Nonclassical Central Limit Theorem”, Math. Notes, 71:4 (2002), 550–555
3. Sh. K. Formanov, “On the Stein–Tikhomirov method and its applications in nonclassical limit theorems”, Discrete Math. Appl., 17:1 (2007), 23–36
4. “Abstracts of Talks Given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172
5. I. A. Ibragimov, E. L. Presman, Sh. K. Formanov, “O modifikatsiyakh uslovii Lindeberga i Rotarya v tsentralnoi predelnoi teoreme”, Teoriya veroyatn. i ee primen., 65:4 (2020), 818–822
•  Number of views: This page: 273 Full text: 101 First page: 1