Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables

The limiting behavior of the maximum partial sums(1/an)max1≤j≤n|∑i=1j‍Xni|is investigated, and some new results are obtained, where{Xni,i≥1,n≥1}is an array of rowwise AANA random variables and{an,n≥1}is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of rowwise AANA random variables is obtained. The results extend and improve the corresponding ones of Hu and Taylor (1997) for arrays of rowwise independent random variables.

On Complete Convergence for Weighted Sums of Arrays of Dependent Random Variables

A rate of complete convergence for weighted sums of arrays of rowwise independent random variables was obtained by Sung and Volodin (2011). In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences ofφ-mixing andρ*-mixing random variables are also obtained. Our results improve and generalize the results of Baek et al. (2008), Kuczmaszewska (2009), and Wang et al. (2010).