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Open Access

Maximal Inequalities for Dependent Random Variables and Applications

Journal of Inequalities and Applications20082008:598319

Received: 16 April 2008

Accepted: 7 July 2008

Published: 9 July 2008


For a sequence of dependent square integrable random variables and a sequence 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 and .


Full ArticlePublisher NoteDependent Random VariableMaximal Inequality

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Authors’ Affiliations

Department of Applied Mathematics, Pai Chai University, Taejon, South Korea


© Soo Hak Sung. 2008

This article is published under license to BioMed Central Ltd. 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.