A central limit theorem for the linear process generated by associated random variables in a Hilbert space

Let {xi(k), k is an element of Z} be a strictly stationary associated sequence of H-valued random variables with E xi(k) = 0 and E parallel to xi(k)parallel to(2) < infinity and (a(k), k is an element of Z) a sequence of linear operators such that Sigma(infinity)(j=0) parallel to a(j)parallel to(L(H)) < infinity. For a linear process X-k = Sigma(infinity)(j=0) a(j)xi(k-j) we derive that Sigma(n)(j=1) X-i/root n satisfies the central limit theorem. (C) 2008 Elsevier B.V. All rights reserved.