The Annals of Probability

Nonstandard limit theorem for infinite variance functionals

Allan Sly and Chris Heyde

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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.

Article information

Ann. Probab., Volume 36, Number 2 (2008), 796-805.

First available in Project Euclid: 29 February 2008

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Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 60G17: Sample path properties 60G18: Self-similar processes

Fractional Brownian motion long-range dependence stable law hypercontractivity


Sly, Allan; Heyde, Chris. Nonstandard limit theorem for infinite variance functionals. Ann. Probab. 36 (2008), no. 2, 796--805. doi:10.1214/07-AOP345.

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