Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables

Let {Xnk,1≤k≤n,n≥1}{Xnk,1≤k≤n,n≥1} be an array of rowwise negatively orthant dependent random variables and let {an,n≥1}{an,n≥1} be a sequence of positive real numbers with an↑∞an↑∞. The convergence properties of partial sums 1an∑k=1nXnk are investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [Hu, T. C., Taylor R. L. (1997). On the strong law for arrays and for the bootstrap mean and variance. International Journal of Mathematics and Mathematical Sciences, 20(2), 375–382].