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A strong law and a law of the single logarithm for arrays of rowwise independent random variables

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  • Chen, Pingyan
  • Ye, Xiaoqin
  • Hu, Tien-Chung

Abstract

Let 1≤p<2. In this paper, we show that there always exist arrays of rowwise independent random variables {Xnk,1≤k≤n,n≥1} with the same distribution as X, such that n−1/p∑k=1nXnk→0a.s . holds if and only if EX=0 and E|X|β<∞ for any β∈(p,2p). This says that the moment gap of the necessary and sufficient condition for the strong law of large numbers between the sequence (β=p) and the array (β=2p) is fulfilled. Analogous results are also obtained for the law of the single logarithm.

Suggested Citation

  • Chen, Pingyan & Ye, Xiaoqin & Hu, Tien-Chung, 2016. "A strong law and a law of the single logarithm for arrays of rowwise independent random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 169-174.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:169-174
    DOI: 10.1016/j.spl.2015.12.009
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