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A note on the almost sure convergence of sums of negatively dependent random variables. (English) Zbl 0925.60024
The results of this paper include the following: a) A necessary and sufficient condition for the validity of the strong law of large numbers when $X$ is an identically distributed sequence of pairwise negative quadrant dependent r.v.’s (a result for r.v.’s with multidimensional indices is also given). b) If $X$ is a sequence of negatively associated r.v.’s with finite second moments, the convergence of the series of the variances implies the almost sure convergence of $\sum_{n=1}^\infty (X_n - EX_n)$. A strong law of large numbers and the sufficiency part of the classical three series theorem are thus extended to this setting.

60F15Strong limit theorems
Full Text: DOI
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