Let, for each n?N, (Xi,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?N0limsup n?+8nSr=NnCov (X0,n, Xr,n)=0;where N0is either infinite or the first positive integer Nfor which the limit of the sum nSr=NnCov (X0,n, Xr,n) vanishes as n goes to infinity. The purpose of this paper is to build, from (Xi,n)0?i?n, a sequence of independent random variables (X˜i,n)0?i?nsuch that the two sumsSi=1nXi,nandSi=1nX˜i,nhave the same asymptotic limiting behavior (in distribution).
Billingsley, P., Probability and measure, Wiley (1986). MR 87f:60001
Newman, C. M., Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Y. L. Tong, editor, Inequalities in Statistics and Probability, IMS Lecture Notes-Monograph Series 5 (1984), 127-140. MR 86i:60072
Inequalities in Statistics and Probability, () 127-140.
Inequalities in Statistics and Probability127140)| false