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Abstract  

We present a generalization of Baum-Katz theorem for negatively associated random variables satisfying some cover condition.

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Let, for each n?N, (X i,n)0 ? i ? nbe a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim N ? N 0limsup n ? + 8 nSr=N nCov (X 0,n, X r,n)=0;where N 0is either infinite or the first positive integer Nfor which the limit of the sum nSr=N nCov (X 0,n, X r,n) vanishes as n goes to infinity. The purpose of this paper is to build, from (X i,n)0 ? i ? n, a sequence of independent random variables (X˜i,n)0 ? i ? nsuch that the two sumsSi =1 n X i,nandSi =1 n X˜i,nhave the same asymptotic limiting behavior (in distribution).

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. [6] Huang , W. 2004 A nonclassical law of the iterated logarithm for functions of negatively associated random variables Stochastic Anal. Appl. 22

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. , Almost sure central limit theorems for strongly mixing and associated random variables , Inter. J. of Math. , 29 ( 3 ) ( 2001 ), 125 – 131 . [5] L ehmann , E. L

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Shao, Q. M. and Su, C. , The law of the iterated logarithm for negatively associated random variables, Stoch. Proc. Appl. , 83 (1) (1999), 139–148. MR 1705604 ( 2000g :60052) Su C

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iterated logarithm for geometrically weighted series of negatively associated random variables Statist. Probab. Lett. 63 133 – 143 10.1016/S0167

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