Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
type: Item
instance of: scholarly article
title: Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
zbMATH Open document ID: 0839.60024
author: Miguel A. Arcones
published in: The Annals of Probability
publication date: 1995-12-20T00:00:00Z
review text: Limit theorems for normalized sums of functions of stationary mean-zero vector-valued Gaussian sequences satisfying long range dependence conditions are considered. Depending on the rate of decay of the correlation coefficients, the limit law is either Gaussian or the law of a multiple Itô-Wiener integral. Also functional versions of these results are obtained. Furthermore, the blockwise bootstrap of these limit theorems in the case when the limit is normal could be proved. The derived limit theorems remain also true (with obvious changes) for stationary Gaussian random fields.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 828385
zbMATH Keywords: stationary Gaussian sequence
zbMATH Keywords: long range dependence
zbMATH Keywords: moving blocks bootstrap
zbMATH Keywords: multiple Ito-Wiener integrals
reviewed by: Lothar Heinrich
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988503
OpenAlex ID: W1970669268
DOI: 10.1214/AOP/1176988503
description: scientific article; zbMATH DE number 828385