On Asymptotic Unbiasedness of the Estimator for the Linear Functional of Spectral Density of Stationary Gaussian Process

For the real-valued stationary Gaussian centered process X(t), t ? R, R = (- ?; + ? ), having a spectral density f(?), a problem of asymptotic unbiasedness is considered for the estimator (statistics) LT = ? ?(?)IT(?)d?, ? ?(- ?; + ? ), where is IT(?) a periodogram of a process, for the linear functional of the spectral density L(f) = ? ?(?)f(?)d? of the stationary Gaussian centered process based on the sample {X (t),0 ? t ? T }.

stationary process, periodogram of a process, spectral density, spectral mean, asymptotic unbiasedness, Feuer singular integral, Feuer kernel