Limiting distributions of nonlinear vector functions of stationary Gaussian processes
type: Item
instance of: scholarly article
title: Limiting distributions of nonlinear vector functions of stationary Gaussian processes
zbMATH Open document ID: 0712.60021
author: Hwai-Chung Ho
author: Tze-Chien Sun
published in: The Annals of Probability
publication date: 1990-01-01T00:00:00Z
review text: Let \((X_ m,Y_ m)\), \(m\in Z\), be a sequence of stationary Gaussian vectors. Let H(x) and K(x) be two real functions and define \[ Z^ n_ H=A_ n^{-1}\sum^{n-1}_{m=0}H(X_ m)\text{ and } Z^ n_ K=B_ n^{-1}\sum^{n-1}_{m=0}K(Y_ m), \] where \(A_ n\) and \(B_ n\) are some constants. The purpose of this paper is to study the joint limiting distribution of \((Z^ n_ H,Z^ n_ K)\). Moreover it is shown that \(Z^ n_ H\) and \(Z^ n_ K\) are asymptotically independent in various cases. Some application of this to the limiting distribution for a certain class of nonlinear infinite-coordinated functions of a Gaussian process is also examined.
reviewed by: N. G. Gamkrelidze
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 4172042
zbMATH Keywords: stationary Gaussian vectors
zbMATH Keywords: asymptotically independent
zbMATH Keywords: Gaussian process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176990740
OpenAlex ID: W2042707279
DOI: 10.1214/AOP/1176990740
description: scientific article; zbMATH DE number 4172042