Precise Rates in Log Laws for NA Sequences
Copyright policy ) Zhao, Yuexu(Institute of Applied Mathematics and Engineering Computation, Hangzhou Dianzi University);
Precise Rates in Log Laws for NA Sequences
LetX1,X2,…be a strictly stationary sequence of negatively associated (NA) random variables withEX1=0, setSn=X1+⋯+Xn, suppose thatσ2=EX12+2∑n=2∞EX1Xn>0andEX12<∞,if−1<α≤1;EX12(log|X1|)α<∞, ifα>1. We provelimε↓0ε2α+2∑n=1∞((logn)α/n)P(|Sn|≥σ(ε+κn)2nlogn)=2−(α+1)(α+1)−1E|N|2α+2, whereκn=O(1/logn)and N is the standard normal random variable.
- Hangzhou Dianzi University China (People's Republic of)
QA1-939, Central limit and other weak theorems, Mathematics
QA1-939, Central limit and other weak theorems, Mathematics
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