The Annals of Probability

Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors

Miguel A. Arcones

Full-text: Open access

Abstract

Limit theorems for functions of stationary mean-zero Gaussian sequences of vectors satisfying long range dependence conditions are considered. Depending on the rate of decay of the coefficients, the limit law can be either Gaussian or the law of a multiple Ito-Wiener integral. We prove the bootstrap of these limit theorems in the case when the limit is normal. A sufficient bracketing condition for these limit theorems to happen uniformly over a class of functions is presented.

Article information

Source
Ann. Probab., Volume 22, Number 4 (1994), 2242-2274.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988503

Digital Object Identifier
doi:10.1214/aop/1176988503

Mathematical Reviews number (MathSciNet)
MR1331224

Zentralblatt MATH identifier
0839.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles 60G10: Stationary processes

Keywords
Long range dependence bootstrap multiple Ito-Wiener integrals moving blocks bootstrap empirical processes stationary Gaussian sequence

Citation

Arcones, Miguel A. Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors. Ann. Probab. 22 (1994), no. 4, 2242--2274. doi:10.1214/aop/1176988503. https://projecteuclid.org/euclid.aop/1176988503


Export citation