On the Brunk-Chung type strong law of large numbers for sequences of blockwise $m$-dependent random variables
ESAIM: Probability and Statistics, Tome 10 (2006), pp. 258-268.

For a sequence of blockwise $m$-dependent random variables $\left\{{X}_{n},n\ge 1\right\}$, conditions are provided under which ${lim}_{n\to \infty }\left({\sum }_{i=1}^{n}{X}_{i}\right)/{b}_{n}=0$ almost surely where $\left\{{b}_{n},n\ge 1\right\}$ is a sequence of positive constants. The results are new even when ${b}_{n}\equiv {n}^{r},r>0$. As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [Proc. Amer. Math. Soc. 101 (1987) 709-715], and Gaposhkin [Teor. Veroyatnost. i Primenen. 39 (1994) 804-812]. The sharpness of the results is illustrated by examples.

DOI : https://doi.org/10.1051/ps:2006010
Classification : 60F15
Mots clés : strong law of large numbers, almost sure convergence, blockwise $m$-dependent random variables
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author = {Thanh, Le Van},
title = {On the {Brunk-Chung} type strong law of large numbers for sequences of blockwise $m$-dependent random variables},
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Thanh, Le Van. On the Brunk-Chung type strong law of large numbers for sequences of blockwise $m$-dependent random variables. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 258-268. doi : 10.1051/ps:2006010. http://www.numdam.org/articles/10.1051/ps:2006010/

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