Nonstandard limit theorem for infinite variance functionals
Allan Sly and Chris Heyde
Source: Ann. Probab.
Volume 36, Number 2
(2008), 796-805.
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 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.
Primary Subjects: 60G15, 60G17, 60G18
Keywords: Fractional Brownian motion; long-range dependence; stable law; hypercontractivity
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1204306968
Digital Object Identifier: doi:10.1214/07-AOP345
Mathematical Reviews number (MathSciNet):
MR2393998
Zentralblatt MATH identifier:
1144.60030
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