We 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.
"Nonstandard limit theorem for infinite variance functionals." Ann. Probab. 36 (2) 796 - 805, March 2008. https://doi.org/10.1214/07-AOP345