Nonstandard limit theorem for infinite variance functionals

Allan Sly; Chris Heyde

doi:10.1214/07-AOP345

Nonstandard limit theorem for infinite variance functionals

Allan Sly, Chris Heyde

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We consider functional 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 Levy 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.

Original language	English (US)
Pages (from-to)	796-805
Number of pages	10
Journal	Annals of Probability
Volume	36
Issue number	2
DOIs	https://doi.org/10.1214/07-AOP345
State	Published - Mar 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Fractional Brownian motion
Hyper-contractivity
Long-range dependence
Stable law

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10.1214/07-AOP345

Cite this

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abstract = "We consider functional 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 Levy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and α-stable L{\'e}vy motion.",

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N2 - We consider functional 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 Levy 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.

AB - We consider functional 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 Levy 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.

KW - Fractional Brownian motion

KW - Hyper-contractivity

KW - Long-range dependence

KW - Stable law

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DO - 10.1214/07-AOP345

M3 - Article

AN - SCOPUS:51949093459

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VL - 36

SP - 796

EP - 805

JO - Annals of Probability

JF - Annals of Probability

IS - 2

ER -

Nonstandard limit theorem for infinite variance functionals

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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