Skip navigation
Skip navigation

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


File Description SizeFormat Image
01_Sly_Nonstandard_limit_theorem_for_2008.pdfPublished Version123.91 kBAdobe PDFThumbnail

Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  20 July 2017/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator