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.


60F15 Strong limit theorems
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