Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 385362, 11 pages
Exponential Inequalities for Positively Associated Random Variables and Applications
1Department of Mathematics, Hunan University of Science and Engineering, Yongzhou, 425100 Hunan, China
2Department of Mathematics, Guangxi Normal University, Guilin, 541004 Guangxi, China
3Department of Physics, Hunan University of Science and Engineering, Yongzhou, 425100 Hunan, China
Received 1 January 2008; Accepted 6 March 2008
Academic Editor: Jewgeni Dshalalow
Copyright © 2008 Guodong Xing et al. 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.
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.