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Precise asymptotics for a new kind of complete moment convergence

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  • Liu, Weidong
  • Lin, Zhengyan

Abstract

In this paper, we introduce a new kind of complete moment convergence, which includes complete convergence as a special case. And we also achieves some results about precise asymptotics for this kind of complete moment convergence. For example, let {X,Xn;n[greater-or-equal, slanted]1} be a sequence of i.i.d. random variables, then holds, if and only if EX=0, EX2=[sigma]2 and .

Suggested Citation

  • Liu, Weidong & Lin, Zhengyan, 2006. "Precise asymptotics for a new kind of complete moment convergence," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1787-1799, October.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:16:p:1787-1799
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    References listed on IDEAS

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    1. Chen, Robert, 1978. "A remark on the tail probability of a distribution," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 328-333, June.
    2. Pruss, Alexander R., 1997. "A two-sided estimate in the Hsu--Robbins--Erdös law of large numbers," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 173-180, October.
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    Cited by:

    1. Xiao, Xiaoyong & Yin, Hongwei, 2012. "Precise asymptotics in the law of iterated logarithm for the first moment convergence of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1590-1596.
    2. He, Jianjun, 2012. "An estimate of the remainder of a limit theorem," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 478-487.
    3. Xie, Tingfan & He, Jianjun, 2012. "Rate of convergence in a theorem of Heyde," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1576-1582.

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