Non-central limit theorems for non-linear functionals of \(k\) Gaussian fields
type: Item
instance of: scholarly article
title: Non-central limit theorems for non-linear functionals of \(k\) Gaussian fields
zbMATH Open document ID: 0770.60025
author: M. V. Sánchez de Naranjo
published in: Journal of Multivariate Analysis
publication date: 1993-05-16T00:00:00Z
review text: Let \(\{X^ 1_ n\},\dots,\{X^ k_ n\}\) be stationary Gaussian processes and \(H\) be a real-valued function of \(k\) variables such that \(E(H(X^ 1_ j,\dots,X_ j^ k))=0\), \(E(H^ 2(X^ 1_ j,\dots,X^ k_ j))<\infty\) and it does not vanish on a set of positive measure. The author considers the limit behavior of the random fields \(A^{-1}_ N\sum^{(n+1)N}_{j=nN}H(X^ 1_ j,\dots,X^ k_ j)\), where \(A_ N\) are appropriate norming constants. The limit distribution is given in terms of a non-Guassian process for some \(H\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 168713
zbMATH Keywords: stationary random fields
zbMATH Keywords: random spectral measure
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: stationary Gaussian processes
MaRDI profile type: Publication
full work available at URL: jmva.1993.1013
OpenAlex ID: W2337187786
DOI: 10.1006/JMVA.1993.1013
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description: scientific article; zbMATH DE number 168713