On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions

We establish conditions of the weak convergence of the empirical correlogram of a stationary Gaussian process to some Gaussian process in the space of continuous functions. We prove that such a convergence holds for a broad class of stationary Gaussian processes with square integrable spectral density.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 11, pp. 1485–1497, November, 1995.This work was financially supported by the Ukrainian State Committee on Science and Technology.