Convergence of Appell polynomials of long range dependent moving averages in martingale differences

We study limit distribution of partial sums S-N,k((t)) = Sigma(s=1)([Nt]) A (k)(X-s) of Appell polynomials of the long-range dependent moving average p rocess X-t = Sigma(i less than or equal to t) b(t-i zeta i), where {zeta(i) } is a strictly stationary and weakly dependent martingale difference seque nce, and b(i) similar to i(d-1) (0 < d < 1 / 2). We show that if k(1 - 2 d) < 1, then suitably normalized partial sums S-N,S-k(t) converge in distribu tion to the kth order Hermite process. This result generalizes the correspo nding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence {zeta(i)}.