Open Access

Maximal Inequalities for Dependent Random Variables and Applications

Journal of Inequalities and Applications20082008:598319

DOI: 10.1155/2008/598319

Received: 16 April 2008

Accepted: 7 July 2008

Published: 9 July 2008

Abstract

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 .

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Authors’ Affiliations

(1)
Department of Applied Mathematics, Pai Chai University

Copyright

© 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.