For random variables and random weights satisfying Marcinkiewicz-Zygmund and Rosenthal type moment inequalities, we establish complete convergence results for randomly weighted sums of the random variables. Our results generalize those of (Thanh et al. SIAM J. Control Optim., 49, 106–124 (2011), Han and Xiang J. Ineq. Appl., 2016, 313 (2016), Li et al. J. Ineq. Appl., 2017, 182 (2017), and Wang et al. Statistics, 52, 503–518 (2018).)

中文翻译：

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满足一些矩不等式的随机变量的随机加权和的完全收敛

对于满足 Marcinkiewicz-Zygmund 和 Rosenthal 型矩不等式的随机变量和随机权重，我们建立了随机变量的随机加权和的完全收敛结果。我们的结果概括了 (Thanh et al. SIAM J. Control Optim., 49, 106–124 (2011), Han and Xiang J. Ineq. Appl., 2016, 313 (2016), Li et al. J. Ineq. . Appl., 2017, 182 (2017), and Wang et al. Statistics, 52, 503–518 (2018).)