Nonstandard limit theorem for infinite variance functionals

Abstract

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 $\alpha$-stable Lévy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and $\alpha$-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)