On the Strong Law of Large Numbers for Weighted Sums of Negatively Superadditive Dependent Random Variables

Abstract

Abstract. Let {Xn, n ≥ 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 1h(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.

On weak law of large numbers for sums of negatively superadditive dependent random variables

“…random variables Jajte proved that {X n − EX n I[|X n | ≤ φ(n)], n ≥ 1} is almost surely summable to 0 by the method (h, g ) if and only if Eφ −1 (|X 1 |) < ∞ (φ −1 is inverse of φ), where g , h and φ(y) = g (y)h(y) are functions satisfying some additional conditions. The most up-to-date survey on this matter may be found in Fazekas et al [7], Naderi et al [13] and Shen [15].…”