2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212382We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is $α$-stable Lévy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and $α$-stable Lévy motion.Published in at http://dx.doi.org/10.1214/07-AOP345 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G15, 60G17, 60G18 (Primary)text