Blazhievska I. Cumulant methods in the estimation of response functions in time-invariant linear systems

Under the assumption that inputs are "close" to a stationary Gaussian white noise, the following results are established: conditions for asymptotic unbiasedness and mean-square consistency of integral-type cross-correlogram estimators; conditions for the asymptotic normality of corresponding estimators and error term in sense of weak convergence of finite-dimensional distributions; conditions for the asymptotic normality of corresponding estimators and error term in sense of weak convergence of distributions in space of continuous functions. Main results are applied to the problem of cross-correlogram estimation of response functions in continuous time-invariant linear systems with the inner noise.