Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 598319, 10 pages
doi:10.1155/2008/598319
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

Recommended by Ondrej Dosly

Abstract

For a sequence {Xn,n≥1} of dependent square integrable random variables and a sequence {bn,n≥1} 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.