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On the strong convergence for weighted sums of asymptotically almost negatively associated random variables. (English) Zbl 1301.60030
Summary: Applying the moment inequality of asymptotically almost negatively associated (AANA, in short) random variables which was obtained by D.-M. Yuan and J. An [Sci. China, Ser. A 52, No. 9, 1887–1904 (2009; Zbl 1184.62099)], some strong convergence results for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of X.-C. Zhou et al. [J. Inequal. Appl. 2011, Article ID 157816, 8 p. (2011; Zbl 1216.60026)], S. H. Sung [Stat. Pap. 52, No. 2, 447–454 (2011; Zbl 1247.60041); ibid. 54, No. 3, 773–781 (2013; Zbl 1307.60023)] to the case of AANA random variables, respectively.

MSC:
60F15 Strong limit theorems
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