On asymptotic behavior of the error term in cross-correlogram estimation of response functions in linear systems

The problem of estimation of an unknown response function of a linear system with inner noises is considered. We suppose that the response function of the system belongs to $L_{2}({\mathbb R})$. Integral-type sample input-output cross-correlograms are taken as estimators of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes that are close, in some sense, to a white noise. Both the asymptotic normality of finite-dimensional distributions of the normalized error term in the cross-correlogram estimation and the asymptotic normality in the space of continuous functions are discussed.