ON A FUNCTIONAL 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=-infinity) parallel to a(j)parallel to(L(H)) < infinity. For a linear process X-k = Sigma(infinity)(j=-infinity)a(j)xi(k-j) we derive that {X-k} fulfills the functional central limit theorem.