Limiting behavior for arrays of row-wise upper extended negatively dependent random variables

Our aim is to obtain deterministic bounds for the row sum elements of a random triangular array introducing, thereunto, a dependence structure for triangular arrays of random variables which extend the concepts of upper and lower extended negatively dependence already known for random variables. Concretely, for triangular arrays { _{Xn, k}, 1 ≦ k≦ n, n≧ 1 } of row-wise upper extended negatively dependent random variables with dominating sequence { _Mn, n≧ 1 } weakly mean dominated by a random variable X and sequences { _bn} of positive constants, conditions are stated to ensure the deterministic boundedness of ^{Σ k= 1 n}(_{Xn, k}- E_{Xn, k}) / _bnLog n, where Log n: = log max { n, e}. In particular, a sufficient moment condition is given permitting us to achieve our goal under the rate of the so called “Law of the Logarithm”.