ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

Title & Authors
ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES
SHEN, AITING;

Abstract
Let {$\small{X_n,n{\geq}1}$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i Keywords negatively superadditive dependent random variables;Marcinkiewicz-Zygmund strong law of large numbers;weighted sums;the three series theorem; Language English Cited by References 1. T. C. Christofides and E. Vaggelatou, A connection between supermodular ordering and positive/negative association, J. Multivariate Anal. 88 (2004), no. 1, 138-151. 2. N. Eghbal, M. Amini, and A. Bozorgnia, Some maximal inequalities for quadratic forms of negative superadditive dependence random variables, Statist. Probab. Lett. 80 (2010), no. 7-8, 587-591. 3. N. Eghbal, On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables, Statist. Probab. Lett. 81 (2011), no. 8, 1112-1120. 4. T. Z. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probab. Statist. 16 (2000), no. 2, 133-144. 5. R. Jajte, On the strong law of large numbers, Ann. Probab. 31 (2003), no. 1, 409-412. 6. B. Y. Jing and H. Y. Liang, Strong limit theorems for weighted sums of negatively associated random variables, J. Theoret. Probab. 21 (2008), no. 4, 890-909. 7. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), no. 1, 286-295. 8. J. H. B. Kemperman, On the FKG-inequalities for measures on a partially ordered space, Nederl. Akad. Wetensch. Proc. Ser. A 80 (1977), no. 4, 313-331. 9. Y. J. Meng and Z. Y. Lin Strong laws of large numbers for$\rho\$-mixing random variables, J. Math. Anal. Appl. 365 (2010), no. 2, 711-717.

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