Journal of the
Korean Mathematical Society JKMS

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.

Keywords: negatively superadditive dependent random variables, Marcinkie\-wicz-Zygmund strong law of large numbers, weighted sums, the three series theorem

MSC numbers: 60F15