Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes
نویسندگان
چکیده
Let X(t), t ∈ R, 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 functionalQT 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 functionalsQT 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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تاریخ انتشار 2007