Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 598319, 10 pages
Research Article

Maximal Inequalities for Dependent Random Variables and Applications

Soo Hak Sung

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

Received 16 April 2008; Revised 3 June 2008; Accepted 7 July 2008

Academic Editor: Ondrej Dosly

Copyright © 2008 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.


For a sequence {Xn,n1} of dependent square integrable random variables and a sequence {bn,n1} of positive numbers, we establish a maximal inequality for weighted sums of dependent random variables. Applying this inequality, we obtain the almost sure convergence of i=1nXi/bi and i=1nXi/bn.