Journal of Applied Mathematics
Volume 2012 (2012), Article ID 329391, 13 pages
http://dx.doi.org/10.1155/2012/329391
Research Article

Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums

Qunying Wu1,2

1College of Science, Guilin University of Technology, Guilin 541004, China
2Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin University of Technology, Guilin 541004, China

Received 18 January 2012; Accepted 7 February 2012

Academic Editor: Naseer Shahzad

Copyright © 2012 Qunying Wu. 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 be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.