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Precise rates in the generalized law of the iterated logarithm

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  • Xiao, Xiao-Yong
  • Zhang, Li-Xin
  • Yin, Hong-Wei
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    Abstract

    Let {X,Xn,n≥1} be a sequence of i.i.d. random variables with EX=0 and 00 and an=o((loglogn)−d), we show the precise rates in the generalized law of the iterated logarithm for a kind of weighted infinite series of P{|Sn|≥(ε+an)σn(loglogn)d}.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 616-623

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:616-623

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    Related research

    Keywords: Precise rates; The law of the iterated logarithm; Complete convergence; i.i.d. random variables;

    References

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    1. Zhang, Yong & Yang, Xiao-Yun, 2008. "Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1051-1055, July.
    2. Wen, Ji-Wei & Zhang, Li-Xin, 2003. "Precise asymptotics in laws of the iterated logarithm for Wiener local time," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 133-145, August.
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