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Journal of Inequalities and Applications
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Exponential Inequalities for Positively Associated Random Variables and Applications

Journal of Inequalities and Applications volume 2008, Article number: 385362 (2008) Cite this article

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 and Affiliations

  1. Department of Mathematics, Hunan University of Science and Engineering, Yongzhou, 425100, Hunan, China

    Guodong Xing

  2. Department of Mathematics, Guangxi Normal University, Guilin, 541004, Guangxi, China

    Shanchao Yang

  3. Department of Physics, Hunan University of Science and Engineering, Yongzhou, 425100, Hunan, China

    Ailin Liu

Authors
  1. Guodong Xing
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  2. Shanchao Yang
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  3. Ailin Liu
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Correspondence to Guodong Xing.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Xing, G., Yang, S. & Liu, A. Exponential Inequalities for Positively Associated Random Variables and Applications. J Inequal Appl 2008, 385362 (2008). https://doi.org/10.1155/2008/385362

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

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