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On complete convergence for weighted sums of arrays of dependent random variables. (English) Zbl 1231.60025

Summary: The rate of complete convergence for weighted sums of arrays of row-wise independent random variables was obtained by S. H. Sung and A. Volodin [Stochastic Anal. Appl. 29, No. 2, 282–291 (2011; Zbl 1217.60007)]. In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences of \(\varphi\)-mixing and \(\rho^\ast\)-mixing random variables are also obtained. Our results improve and generalize the results of J.-I. Baek, M.-H. Ko and T.-S. Kim [J. Korean Math. Soc. 45, No. 4, 1101–1111 (2008; Zbl 1148.60012)], A. Kuczmaszewska [Stat. Probab. Lett. 79, No. 1, 116–124 (2009; Zbl 1154.60319)] and X. Wang et al. [J. Inequal. Appl. 2010, Article ID 372390 (2010; Zbl 1208.60031)].

MSC:

60F15 Strong limit theorems
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