On the Asymptotic Independent Representations for Sums of Some Weakly Dependent Random Variables

Abstract

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 n X 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… (More)

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