On the asymptotic independent representations for sums of some weakly dependent random variables
2006 ◽
Vol 43
(1)
◽
pp. 33-46
Keyword(s):
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).
1981 ◽
Vol 20
(3)
◽
pp. 244-249
◽
1983 ◽
Vol s2-27
(1)
◽
pp. 185-192
1992 ◽
Vol 36
(4)
◽
pp. 783-792
◽
1988 ◽
Vol 27
(4)
◽
pp. 359-368
◽
1977 ◽
Vol 17
(3)
◽
pp. 313-320
◽