Functional limit theorems for Toeplitz quadratic functionals of continuous time Gaussian stationary processes

The paper establishes weak convergence in C[0,1] of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both central and non-central functional limit theorems are obtained.

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Bibliographic Details
Published in:Statistics & probability letters 2015-09, Vol.104, p.58-67
Main Authors: Bai, Shuyang, Ginovyan, Mamikon S., Taqqu, Murad S.
Format: Article
Language:English
Subjects:
Brownian motion
Long memory
Noncentral limit theorem
Stationary Gaussian process
Toeplitz-type quadratic functional
Wiener–Itô integral
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Description
Summary:The paper establishes weak convergence in C[0,1] of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both central and non-central functional limit theorems are obtained.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2015.04.030