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Nourdin et al. [9] established the following universality result: if asequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normalrandom variables converges in distribution to a normal, then the convergencealso holds if one replaces these i.i.d. standard normal random variables in thepolynomial forms by any independent standardized random variables withuniformly bounded third absolute moment. The result, which was stated forpolynomial forms with a finite number of terms, can be extended to allow aninfinite number of terms in the polynomial forms. Based on a contractioncriterion derived from this extended universality result, we prove a centrallimit theorem for a strongly dependent nonlinear processes, whose memoryparameter lies at the boundary between short and long memory.

The universality of homogeneous polynomial forms and critical limits