Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1151780 | Statistics & Probability Letters | 2015 | 5 Pages |
Abstract
Let {X,Xn≥1}{X,Xn≥1} be a sequence of independent and identically distributed random variables with EX=0EX=0 and EX2=1EX2=1. Let α(n)=EX2I(|X|>nloglogn)/EX2I(|X|≤nloglogn), n≥1n≥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
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Xiangdong Liu, Hui Guo,