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On strong convergence for weighted sums of a class of random variables. (English) Zbl 1279.60041

Summary: Let \(\{X_n, n \geq 1\}\) be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of X.-C. Zhou et al. [J. Inequal. Appl. 2011, Article ID 157816, 8 p. (2011; Zbl 1216.60026)] and improves the corresponding one of X. Wang et al. [Discrete Dyn. Nat. Soc. 2011, Article ID 717126, 11 p. (2011; Zbl 1235.60026)] and Q. Wu [J. Appl. Math. 2012, Article ID 104390, 10 p. (2012; Zbl 1253.60046)].

MSC:

60F15 Strong limit theorems
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