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  • Research Article
  • Open Access

Maximal Inequalities for Dependent Random Variables and Applications

Journal of Inequalities and Applications20082008:598319

https://doi.org/10.1155/2008/598319

  • Received: 16 April 2008
  • Accepted: 7 July 2008
  • Published:

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 .

Keywords

  • Full Article
  • Publisher Note
  • Dependent Random Variable
  • Maximal Inequality

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Applied Mathematics, Pai Chai University, Taejon, 302-735, South Korea

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.

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