Journal of Probability and Statistics
Volume 2009 (2009), Article ID 873274, 7 pages
doi:10.1155/2009/873274
Research Article

A Note on Strong Convergence of Sums of Dependent Random Variables

Tien-Chung Hu1 and Neville C. Weber2

1Department of Mathematic, National Tsing Hua University, Hsinchu 30043, Taiwan
2School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW 2006, Australia

Received 5 August 2009; Revised 25 November 2009; Accepted 3 December 2009

Academic Editor: Mohammad Fraiwan Al-Saleh

Copyright © 2009 Tien-Chung Hu and Neville C. Weber. 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

For a sequence of dependent square-integrable random variables and a sequence of positive constants {bn,  n≥1}, conditions are provided under which the series ∑i=1n(Xi−EXi)/bi converges almost surely as n→∞. These conditions are weaker than those provided by Hu et al. (2008).