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

Shuyang Bai, Mamikon S. Ginovyan and Murad S. Taqqu

Statistics & Probability Letters, 2015, vol. 104, issue C, 58-67

Abstract: 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.

Keywords: Stationary Gaussian process; Toeplitz-type quadratic functional; Brownian motion; Noncentral limit theorem; Long memory; Wiener–Itô integral (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.04.030

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