Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables (Communications in Mathematical Research, 2021)
By using Rosenthal type moment inequality for extended negatively dependent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent randomvariables under more general conditions. These results complement and improve thecorresponding results obtained by Li et al. (Li D L, RAO M B, Jiang T F, Wang XC. Complete convergence and almost sure convergence of weighted sums of randomvariables. J. Theoret. Probab., 1995, 8: 49–76) and Liang (Liang H Y. Completeconvergence for weighted sums of negatively associated random variables. Statist.Probab. Lett., 2000, 48: 317–325).
Keywords: extended negatively dependent random variable; complete convergence; weighted sum.