Complete convergence for randomly weighted sums of random variables satisfying some moment inequalities. (English) Zbl 1469.60091
Summary: 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 [Le Van Thanh et al., SIAM J. Control Optim. 49, No. 1, 106–124 (2011; Zbl 1219.93139); J. Han and Y. Xiang, J. Inequal. Appl. 2016, Paper No. 313, 13 p. (2016; Zbl 1353.60026); P. Li et al., J. Inequal. Appl. 2017, Paper No. 182, 16 p. (2017; Zbl 1373.60061)], and [X. Wang et al., Statistics 52, No. 3, 503–518 (2018; Zbl 1391.60055)].
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