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An analogue for Marcinkiewicz–Zygmund strong law of negatively associated random variables

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Abstract

In this paper, we shall establish a new almost sure convergence of negatively associated sequence under the assumption \(\mathbb {E}( |X|^p\log ^{-\alpha } |X|)\) for some \(\alpha \ge 0\) and \(p\in (0,2)\), from which the classic Marcinkiewicz–Zygmund strong law of large numbers is deduced. We further point out that the above moment condition is also necessary for the almost sure convergence.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, China

    Yu Miao, Jianyong Mu & Jie Xu

Authors
  1. Yu Miao
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  2. Jianyong Mu
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  3. Jie Xu
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Correspondence to Yu Miao.

Additional information

This work is supported by IRTSTHN (14IRTSTHN023), NSFC (11471104), NCET (NCET-11-0945).

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Miao, Y., Mu, J. & Xu, J. An analogue for Marcinkiewicz–Zygmund strong law of negatively associated random variables. RACSAM 111, 697–705 (2017). https://doi.org/10.1007/s13398-016-0320-4

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  • DOI: https://doi.org/10.1007/s13398-016-0320-4

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