Precise rates in the law of the iterated logarithm under dependence assumptions

Authors
Liu, Wei Dong Yan Lin, Zheng
Citation
Liu, Wei Dong et Yan Lin, Zheng, Precise rates in the law of the iterated logarithm under dependence assumptions, Acta mathematica Sinica. English series (Print) , 24(1), 2008, pp. 59-74
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
24
Issue
1
Year of publication
2008
Pages
59 - 74
Database
ACNP
SICI code
Abstract
Let {X,X 1,X 2,...} be a strictly stationary .-mixing sequence which satisfies EX = 0, EX 2(log2 |X|)2 < . and .(n) = O(1/(log n)T) for some T > 2. Let S n = . n k=1 X k and a n = O(.n/(log2 n).) for some . > 1/2. We prove that lim..2..2.2.......n=3.1nP(|Sn|..ES2nlog2n.........+an)=2... . The results of Gut and Sp.taru (2000) are special cases of ours