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Let $\{X_n, n\geq1\}$ be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums $\frac{1}{g(n)}\sum_{i=1}^n\frac{X_i}{h(i)}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.
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참고문헌 (22)
참고문헌 신청
T. C. Christofides / 2004 / A connection between supermodular ordering and positive/negative association / J. Multivariate Anal 88(1):138~151
N. Eghbal / 2010 / Some maximal inequalities for quadratic forms of negative superadditive dependence random variables / Statist. Probab. Lett 80(7-8):587~591
N. Eghbal / 2011 / On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables / Statist. Probab. Lett 81(8):1112~1120
T. Z. Hu / 2000 / Negatively superadditive dependence of random variables with applications / Chinese J. Appl. Probab. Statist 16(2):133~144
R. Jajte / 2003 / On the strong law of large numbers / Ann. Probab 31(1):409~412
N. Eghbal / 2010 / Some maximal inequalities for quadratic forms of negative superadditive dependence random variables / Statist. Probab. Lett 80(7-8):587~591
N. Eghbal / 2011 / On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables / Statist. Probab. Lett 81(8):1112~1120
T. Z. Hu / 2000 / Negatively superadditive dependence of random variables with applications / Chinese J. Appl. Probab. Statist 16(2):133~144
R. Jajte / 2003 / On the strong law of large numbers / Ann. Probab 31(1):409~412
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