This article is cited in 21 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

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, 15:3, 509–514

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