LIMIT-THEOREMS FOR BIVARIATE APPELL POLYNOMIALS - PART II - NONCENTRAL LIMIT-THEOREMS

Let (X-t, t is an element of Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low freq uencies. This includes situations, known as strong (or long-range) dep endence, where the spectral density diverges at the origin. We study q uadratic forms of bivariate Appell polynomials of the sequence (X-t) a nd provide general conditions for these quadratic forms, adequately no rmalized, to converge to a non-Gaussian distribution, We consider, in particular, circumstances where strong and weak dependence interact. T he limit is expressed in terms of multiple Wiener-Ito integrals involv ing correlated Gaussian measures.