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Teor. Veroyatnost. i Primenen., 1970, Volume 15, Issue 3, Pages 520–527 (Mi tvp1860)  

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

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.

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English version:
Theory of Probability and its Applications, 1970, 15:3, 509–514

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Received: 03.06.1969

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://www.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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