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Maximal Inequalities for Dependent Random Variables and Applications

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 .

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Correspondence to Soo Hak Sung.

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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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Sung, S.H. Maximal Inequalities for Dependent Random Variables and Applications. J Inequal Appl 2008, 598319 (2008). https://doi.org/10.1155/2008/598319

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

Keywords

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