### ON ASYMPTOTIC BEHAVIOR OF CROSS-CORRELOGRAM ESTIMATORS OF RESPONSE FUNCTIONS IN LINEAR VOLTERRA SYSTEMS

**V. V. BULDYGIN AND I. P. BLAZHIEVSKA**

*Theory of Stochastic Processes*

*Vol.15 (31), no.2, 2009, pp.62-83*

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 $L_{2}(\bf{R})$. 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 close, in some sense, to a white noise. Both the asymptotic normality of finite-dimensional distributions of the centered estimators and their asymptotic normality in the space of continuous functions are studied.