Copyright © 2010 Qing-pei Zang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let {X,Xn;n≥1} be a sequence of independent and identically distributed (i.i.d.) random variables, and X is in the domain of the normal law and EX=0. In this paper, we obtain a general law of complete moment convergence for self-normalized sums.