For a,..., a C and t,..., t 0,

Already the following was shown in [24]. Let X, Y , and W be as above with F(x, y) = x + y, and suppose that X satisfies all of the hypotheses of Theorem 4.1. Suppose that W is stationary and uncorrelated with X and has covariance Kw(t) tending to zero at infinity and uniformly bounded fourth moments. Then the estimator µ n , N( ) constructed for the observed process Y in Theorem 4.1 converges in the sense of Theorem 4.1 to the discrete part of the associated spectral measure of X.