Exponential Inequalities for Positively Associated Random Variables and Applications

Journal of Inequalities and Applications. 2008;2008(1):385362


Journal Homepage

Journal Title: Journal of Inequalities and Applications

ISSN: 1029-242X (Online)

Publisher: SpringerOpen

LCC Subject Category: Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

Full-text formats available: PDF, HTML



Yang Shanchao

Liu Ailin

Xing Guodong


Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 13 weeks


Abstract | Full Text

<p>Abstract</p> <p>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 <inline-formula> <graphic file="1029-242X-2008-385362-i1.gif"/></inline-formula> 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 <inline-formula> <graphic file="1029-242X-2008-385362-i2.gif"/></inline-formula> derived by Oliveira (2005) for the above case.</p>