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A limit theorem related to the Hartman–Wintner–Strassen LIL and the Chover LIL

Author

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  • Li, Deli
  • Zhang, Shuhua

Abstract

Let {X,Xn;n≥1} be a sequence of i.i.d. real-valued random variables, and let Sn=∑i=1nXi,n≥1. Write logx=loge(e∨x), x≥0. In this note we establish a limit theorem which is related to the classical Hartman–Wintner–Strassen law of the iterated logarithm and the classical Chover law of the iterated logarithm. That is, for 1≤p<∞, we show that lim supn→∞|Snn|(logloglogn)−1=ep/2almost surely if and only if EX=0andinf{b>0:limx→∞(loglogx)1−bE(X2I(|X|≤x))=0}=p.

Suggested Citation

  • Li, Deli & Zhang, Shuhua, 2016. "A limit theorem related to the Hartman–Wintner–Strassen LIL and the Chover LIL," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 16-21.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:16-21
    DOI: 10.1016/j.spl.2015.10.007
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    Cited by:

    1. Zou, Yuye & Liu, Xiangdong, 2017. "An extension of a theorem of Mikosch," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 81-86.

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