%0 Journal Article
%T Nonstandard limit theorem for infinite variance functionals
%A Allan Sly
%A Chris Heyde
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/07-AOP345
%X 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 L\'{e}vy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and $\alpha$-stable L\'{e}vy motion.
%U http://arxiv.org/abs/0804.2588v1