Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes |
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| Authors: | M S Ginovyan A A Sahakyan |
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| Institution: | (1) Department of Mathematics and Statistics, MCS 222, Boston University, 111 Cummington Street, Boston, MA 02215, USA;(2) Institute of Mathematics of Armenian National Academy of Sciences, Marshal Bagramian Ave 24-B, 375019 Yerevan, Armenia |
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| Abstract: | Let X(t),  , be a centered real-valued stationary Gaussian process with spectral density f(λ). The paper considers a question concerning asymptotic distribution of Toeplitz type quadratic functional Q
T
of the process X(t), generated by an integrable even function g(λ). Sufficient conditions in terms of f(λ) and g(λ) ensuring central limit theorems for standard normalized quadratic functionals Q
T
are obtained, extending the results of Fox and Taqqu (Prob. Theory Relat. Fields 74: 213–240, 1987), Avram (Prob. Theory
Relat. Fields 79:37–45, 1988), Giraitis and Surgailis (Prob. Theory Relat. Fields 86: 87–104, 1990), Ginovian and Sahakian
(Theory Prob. Appl. 49:612–628, 2004) for discrete time processes.
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| Keywords: | Stationary Gaussian process Spectral density Toeplitz type quadratic functional Central limit theorems |
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