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Nonstandard limit theorem for infinite variance functionals

Sly, Allan; Heyde, Chris


We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the longrange 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.

CollectionsANU Research Publications
Date published: 2008
Type: Journal article
Source: The Annals of Probability
DOI: 10.1214/07-AOP345
Access Rights: Open Access


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