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

Pingyan Chen, Xiaoqin Ye and Tien-Chung Hu

Statistics & Probability Letters, 2016, vol. 110, issue C, 169-174

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.

Keywords: Sequence; Array; Rowwise independent; Strong law of large numbers; Law of the single logarithm (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2015.12.009

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