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

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Date Issued
2015-09-01
Publisher Version
10.1016/j.spl.2015.04.030
Author(s)
Bai, Shuyang
Ginovyan, Mamikon S.
Taqqu, Murad S.
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https://hdl.handle.net/2144/37510
Version
Accepted manuscript
Citation (published version)
Shuyang Bai, Mamikon S Ginovyan, Murad S Taqqu. 2015. "Functional limit theorems for Toeplitz quadratic functionals of continuous time Gaussian stationary processes." STATISTICS & PROBABILITY LETTERS, Volume 104, pp. 58 - 67 (10). https://doi.org/10.1016/j.spl.2015.04.030
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.
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