Abstract
Let, for each
n
?N, (
X
i,n
)
0
?
i
?
n
be a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim
N
?
N
0
limsup
n
?
+
8
n
S
r=N
n
Cov (
X
0,
n
,
X
r,n
)=0;where
N
0
is either infinite or the first positive integer
N
for which the limit of the sum
n
S
r=N
n
Cov (
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
?
n
such that the two sumsS
i
=1
n
X
i,n
andS
i
=1
n
X
˜
i,n
have the same asymptotic limiting behavior (in distribution).