An extension on the rate of complete moment convergence for weighted sums of weakly dependent random variables

Abstract

<abstract><p>The authors study the convergence rate of complete moment convergence for weighted sums of weakly dependent random variables without assumptions of identical distribution. Under the moment condition of $ E{{{\left| X \right|}^{\alpha }}}/{{{\left(\log \left(1+\left| X \right| \right) \right)}^{\alpha /\gamma -1}}}\; < \infty $ for $ 0 < \gamma < \alpha $ with $ 1 < \alpha \le 2 $, we establish the complete $ \alpha $-th moment convergence theorem for weighted sums of weakly dependent cases, which improves and extends the related known results in the literature.</p></abstract>