Convergence properties for weighted sums of NSD random variables |
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Authors: | Aiting Shen Xinghui Wang Huayan Zhu |
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Affiliation: | 1. School of Mathematical Science, Anhui University, Hefei, Chinashenaiting114@126.com;3. School of Mathematical Science, Anhui University, Hefei, China |
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Abstract: | AbstractLet {Xn, n ? 1} be a sequence of negatively superadditive dependent (NSD, in short) random variables and {bni, 1 ? i ? n, n ? 1} be an array of real numbers. In this article, we study the strong law of large numbers for the weighted sums ∑ni = 1bniXi without identical distribution. We present some sufficient conditions to prove the strong law of large numbers. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for NSD random variables is obtained. In addition, the complete convergence for the weighted sums of NSD random variables is established. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables. |
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Keywords: | Negatively superadditive-dependent random variables Weighted sums Marcinkiewicz-Zygmund strong law of large numbers Complete convergence. |
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