A note on the Davis–Gut law

Xiangdong Liu and Hui Guo

Statistics & Probability Letters, 2015, vol. 105, issue C, 163-167

Abstract: Let {X,Xn≥1} be a sequence of independent and identically distributed random variables with EX=0 and EX2=1. Let α(n)=EX2I(|X|>nloglogn)/EX2I(|X|≤nloglogn), n≥1. In this note, a supplement to the Davis–Gut law is provided by proving that ∑n=1∞n−1{|∑k=1nXk|>2nloglogn}<∞ or =∞ according to ∑n=1∞(nlognloglogn)−1⋅(logn)−α(n)<∞ or =∞. An example is given for illustrating the obtained result.

Keywords: Davis–Gut law; Law of the iterated logarithm (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.06.018

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