On Estimation of Convergence Rate of Statistics Expectancy LT to Linear Functional of Spectral Density L(f) of Stationary Gaussian Process

For the real-valued stationary Gaussian centered process X(t), having a spectral density f(λ), a problem is considered of estimating the convergence rate of expectancy of statistics L_T = S ϕ(λ)I_T(λ)dλ, where IT(λ) is a periodogram of a process X(t), to a linear functional of the spectral density L(f) = S ϕ(λ)f(λ)dλ of the stationary Gaussian process based on the sample {X(t), 0 ≤ t ≤ T}.