We study limit distributions of sums S-N((G)) = Sigma(t=1)(N) G(X-t) of non
linear functions G(x) in stationary variables of the form X-t = Y-t + Z(t),
where {Y-t} is a linear (moving average) sequence with long-range dependen
ce, and {Z(t)} is a (nonlinear) weakly dependent sequence. In particular, w
e consider the case when {Y-t} is Gaussian and either (1) {Z(t)} is a weakl
y dependent multilinear form in Gaussian innovations, or (2) {Z(t)} is a fi
nitely dependent functional in Gaussian innovations or (3) {Z(t)} is weakly
dependent and independent of {Y-t}. We show in all three cases that the li
mit distribution of S-N((G)) is determined by the Appell rank of G(x), or t
he lowest k greater than or equal to 0 such that a(k) = a(k) E{G(X-0 + c)}/
ac(k)\(c=0) not equal 0.