  Nourdin et al. [9] established the following universality result: if a
sequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normal
random variables converges in distribution to a normal, then the convergence
also holds if one replaces these i.i.d. standard normal random variables in the
polynomial forms by any independent standardized random variables with
uniformly bounded third absolute moment. The result, which was stated for
polynomial forms with a finite number of terms, can be extended to allow an
infinite number of terms in the polynomial forms. Based on a contraction
criterion derived from this extended universality result, we prove a central
limit theorem for a strongly dependent nonlinear processes, whose memory
parameter lies at the boundary between short and long memory.
