COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF SEQUENCES OF NEGATIVELY DEPENDENT RANDOM VARIABLES

This paper is a theoretical contribution on the complete convergence of partial sums. Let $ \lbrace X_n, n \geq 1 \rbrace$ be a sequence of non negatively dependent random, which is stochastically dominated by a random variable $X$ and $\lbrace \ \Psi_{ni} ; 1\leq i \leq n, n\geq 1\rbrace $ be a an array of random variables. Under mild condition we establish the complete convergence for weighted sums $\sum_{i=1}^j \Psi_{ni}X_i $. This result obtained with random coefficients generalizes the work of those obtained with real coefficients [12-14,16]. Our results also generalize those on complete convergence theorem previously obtained from the independent and identically distributed case to negatively dependent.