Complete convergence of weighted sums for arrays of rowwise $\varphi $-mixing random variables

[摘要] In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise $\varphi $-mixing random variables, and the Baum-Katz-type result for arrays of rowwise $\varphi $-mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of $\varphi $-mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).

[学科分类] 应用数学

[关键词] complete convergence;$\varphi $-mixing sequence;Marcinkiewicz-Zygmund type strong law of large numbers