On complete convergence for weighted sums of arrays of dependent random variables
Summary: The rate of complete convergence for weighted sums of arrays of row-wise independent random variables was obtained by \textit{S. H. Sung} and \textit{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 \textit{J.-I. Baek, M.-H. Ko} and \textit{T.-S. Kim} [J. Korean Math. Soc. 45, No.~4, 1101--1111 (2008; Zbl 1148.60012)], \textit{A. Kuczmaszewska} [Stat. Probab. Lett. 79, No.~1, 116--124 (2009; Zbl 1154.60319)] and \textit{X. Wang} et al. [J. Inequal. Appl. 2010, Article~ID 372390 (2010; Zbl 1208.60031)].
negatively associated and negatively dependent random variables
\(\varphi\)-mixing and \(\rho^\ast\)-mixing random variables
scientific article; zbMATH DE number 5997813
scientific article