Convergence properties of the maximal partial sums for arrays of rowwise na random variables

摘要

Let {X _(nk), 1 ≦ k ≦ n, n ≧ 1} be an array of rowwise negatively associated (NA) random variables, and let {a _n, n ≧ 1} be a sequence of positive real numbers with a _n ↑ ∞. The convergence properties of maximal partial sums a _n ~(-1) max _(1≦j≦n) |Σ ~j k=1 X _(nk)| are investigated, and some new results are obtained. The results extend and improve the corresponding theorems by Gan and Chen.