A Kind of Complete Moment Convergence for Sums of Independent and Nonidentically Distributed Random Variables

Abstract

Let $\{X,X_n,n\ge 1\}$ be a sequence of independent and nonidentically distributed random variables. We obtain a new kind of complete moment convergence for their sums under the Lyapunov condition. Moreover, our result extends and improves the corresponding result of the independent and identically distributed (i.i.d.) cases.