Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 89107, 11 pages
Research Article

Precise Rates in Log Laws for NA Sequences

Yuexu Zhao

Institute of Applied Mathematics and Engineering Computation, Hangzhou Dianzi University, Hangzhou 310018, China

Received 27 September 2006; Revised 23 December 2006; Accepted 30 January 2007

Copyright © 2007 Yuexu Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X1,X2, be a strictly stationary sequence of negatively associated (NA) random variables with EX1=0, set Sn=X1++Xn, suppose that σ2=EX12+2n=2EX1Xn>0 and EX12<, if 1<α1; EX12(log|X1|)α<, if α>1. We prove limε0ε2α+2n=1((logn)α/n)P(|Sn|σ(ε+κn)2nlogn)=2(α+1)(α+1)1E|N|2α+2, where κn=O(1/logn) and N is the standard normal random variable.