the almost sure convergence for weighted sums of linear negatively dependent random variables

in this paper, we generalize a theorem of shao [12] by assuming that is a sequence of linear negatively dependent random variables. also, we extend some theorems of chao [6] and thrum [14]. it is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of real numbers. moreover, we prove the almost sure convergence for weighted sums , when is a sequence of pairwise negative quadrant dependence stochastically bounded random variables under some suitable conditions on .