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March 2008 Nonstandard limit theorem for infinite variance functionals
Allan Sly, Chris Heyde
Ann. Probab. 36(2): 796-805 (March 2008). DOI: 10.1214/07-AOP345


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.


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Allan Sly. Chris Heyde. "Nonstandard limit theorem for infinite variance functionals." Ann. Probab. 36 (2) 796 - 805, March 2008.


Published: March 2008
First available in Project Euclid: 29 February 2008

zbMATH: 1144.60030
MathSciNet: MR2393998
Digital Object Identifier: 10.1214/07-AOP345

Primary: 60G15 , 60G17 , 60G18

Keywords: fractional Brownian motion , hypercontractivity , long-range dependence , Stable law

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 2 • March 2008
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