The Annals of Probability

Limiting Distributions of Nonlinear Vector Functions of Stationary Gaussian Processes

Hwai-Chung Ho and Tze-Chien Sun

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Abstract

Given a stationary Gaussian vector process $(X_m, Y_m), m \in Z$, and two real functions $H(x)$ and $K(x)$, we define $Z^n_H = A^{-1}_n\sum^{n - 1}_{m = 0} H(X_m)$ and $Z^n_K = B^{-1}_n\sum^{n - 1}_{m = 0} K(Y_m)$, where $A_n$ and $B_n$ are some appropriate constants. The joint limiting distribution of $(Z^n_H, Z^n_K)$ is investigated. It is shown that $Z^n_H$ and $Z^n_K$ are asymptotically independent in various cases. The application of this to the limiting distribution for a certain class of nonlinear infinite-coordinated functions of a Gaussian process is also discussed.

Article information

Source
Ann. Probab., Volume 18, Number 3 (1990), 1159-1173.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990740

Digital Object Identifier
doi:10.1214/aop/1176990740

Mathematical Reviews number (MathSciNet)
MR1062063

Zentralblatt MATH identifier
0712.60021

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G15: Gaussian processes

Keywords
Central limit theorem noncentral limit theorem long-range dependence stationary Gaussian vector processes

Citation

Ho, Hwai-Chung; Sun, Tze-Chien. Limiting Distributions of Nonlinear Vector Functions of Stationary Gaussian Processes. Ann. Probab. 18 (1990), no. 3, 1159--1173. doi:10.1214/aop/1176990740. https://projecteuclid.org/euclid.aop/1176990740


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