On the strong law of large numbers for weighted sums of negatively superadditive dependent random variables
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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.
Abstract
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.
참고문헌 (22)
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