Open Access

Exponential Inequalities for Positively Associated Random Variables and Applications

Journal of Inequalities and Applications20082008:385362

https://doi.org/10.1155/2008/385362

Received: 1 January 2008

Accepted: 6 March 2008

Published: 6 March 2008

Abstract

We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005). By one of the inequalities, we obtain the convergence rate for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm and improves the convergence rate derived by Oliveira (2005) for the above case.

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Authors’ Affiliations

(1)
Department of Mathematics, Hunan University of Science and Engineering
(2)
Department of Mathematics, Guangxi Normal University
(3)
Department of Physics, Hunan University of Science and Engineering

Copyright

© Guodong Xing et al. 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.