ON THE ASYMPTOTIC INDEPENDENT REPRESENTATIONS FOR SUMS OF SOME WEAKLY DEPENDENT RANDOM VARIABLES

Journal Article

• نوع عمل المنشور: Paper
• رابط المنشور على الويب: RAFIK AGUECH , SANA LOUHICHI and SOFYEN LOUHICHI
• المجلة \ الصحيفة: Studia Scientiarum Mathematicarum Hungarica
• رقم العدد: 1
• رقم الإصدار السنوي: 43
• الصفحات: 33–46

مستخلص المنشور

Let, for each n ∈ N, (Xi,n) 05i5n be a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim N→N0 lim sup n→+∞ n Xn r=N Cov (X0,n, Xr,n) = 0; where N0 is either infinite or the first positive integer N for which the limit of the sum n Pn r=N Cov (X0,n, Xr,n) vanishes as n goes to infinity. The purpose of this paper is to build, from (Xi,n) 05i5n , a sequence of independent random variables (X˜i,n) 05i5n such that the two sums Pn i=1 Xi,n and Pn i=1 X˜i,n have the same asymptotic limiting behavior (in distribution).