Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 957056, 10 pages
doi:10.1155/2009/957056
Research Article

A Limit Theorem for the Moment of Self-Normalized Sums

Qing-pei Zang

Department of Mathematics, Huaiyin Teachers College, Huaian 223300, China

Received 25 December 2008; Revised 30 March 2009; Accepted 18 June 2009

Academic Editor: Jewgeni Dshalalow

Copyright © 2009 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 attraction of the normal law and EX=0. For 1≤p<2,b>−1, we prove the precise asymptotics in Davis law of large numbers for ∑n=1∞((logn)b/n)E{(|Sn|/Vn)−ε(2logn)(2−p)/(2p)}+ as ε↘0.