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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.

##### MSC:
 60F15 Strong limit theorems
Full Text:
##### References:
 [1] Birkel, T.: A note on the strong law of large numbers for positively dependent random variables. Statist. probab. Lett. 7, 17-20 (1989) · Zbl 0661.60048 [2] Esary, J.; Proschan, F.; Walkup, D.: Association of random variables with applications. Ann. math. Statist. 38, 1466-1474 (1967) · Zbl 0183.21502 [3] Etemadi, N.: An elementary proof of the strong law of large numbers. Z. wahrsch. Verw. gebiete 55, 119-122 (1981) · Zbl 0438.60027 [4] Etemadi, N.: On the strong law of large numbers for nonnegative random variables. J. multivariate anal. 13, 187-193 (1983) · Zbl 0524.60033 [5] Joag-Dev, K.; Proschan, F.: Negative association of random variables with applications. Ann. statist. 11, 286-295 (1983) · Zbl 0508.62041 [6] Lehmann, E. L.: Some concepts of dependence. Ann. math. Statist. 37, 1137-1153 (1966) · Zbl 0146.40601 [7] Newman, C. M.: Asymptotic independence and limit theorems for positively and negatively dependent random variables. Inequalities in statistics and probability, 127-140 (1984) [8] Petrov, W. W.: Limit theorems for sums of independent random variables. (1987) · Zbl 0621.60022