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Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 3, Pages 520–527 (Mi tvp1860)  
This article is cited in 20 scientific papers (total in 20 papers)

Short Communications

On the strong law of large numbers and the law of the iterated logarithm for a sequence of independent random variables

V. A. Egorov

Leningrad
Full-text PDF (357 kB) Citations (20)
Abstract: Let $\{X_n\}$ be a sequence of independent random variables with zero means and finite variances, $\{b_n\}$ be an increasing sequence of positive numbers, $b_n\to\infty$, $X_n=o(b_n)$ a.s. Some new conditions are found which are sufficient for the equality $\sum_{j=1}^nX_j=o(b_n)$ a.s. These conditions are expressed in terms of second moments. New sufficient conditions for the law of the iterated logarithm are also obtained.
Received: 03.06.1969
English version:
Theory of Probability and its Applications, 1970, Volume 15, Issue 3, Pages 509–514
DOI: https://doi.org/10.1137/1115053
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Egorov, “On the strong law of large numbers and the law of the iterated logarithm for a sequence of independent random variables”, Teor. Veroyatnost. i Primenen., 15:3 (1970), 520–527; Theory Probab. Appl., 15:3 (1970), 509–514
Citation in format AMSBIB
\Bibitem{Ego70}
\by V.~A.~Egorov
\paper On the strong law of large numbers and the law of the iterated logarithm for a~sequence of independent random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 3
\pages 520--527
\mathnet{http://mi.mathnet.ru/tvp1860}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=283852}
\zmath{https://zbmath.org/?q=an:0205.45104}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 3
\pages 509--514
\crossref{https://doi.org/10.1137/1115053}
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    • This publication is cited in the following 20 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
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