Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 271265, 14 pages
Research Article

Moment Inequalities and Complete Moment Convergence

Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South Korea

Received 22 August 2009; Accepted 26 September 2009

Academic Editor: Andrei Volodin

Copyright © 2009 Soo Hak Sung. 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.


Let {Yi,1in} and {Zi,1in} be sequences of random variables. For any ϵ>0 and a>0, bounds for E(|i=1n(Yi+Zi)|ϵa)+ and E(max1kn|i=1k(Yi+Zi)|ϵa)+ are obtained. From these results, we establish general methods for obtaining the complete moment convergence. The results of Chow (1988), Zhu (2007), and Wu and Zhu (2009) are generalized and extended from independent (or dependent) random variables to random variables satisfying some mild conditions. Some applications to dependent random variables are discussed.