On asymptotic behavior of cross-correlogram estimators of response functions in linear Volterra systems

V. V. Buldygin ; I. P. Blazhievska

Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 84-98.

Résumé

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.

Détail

Keywords: Response function, sample cross-correlogram, integral involving a cyclic product of kernels, asymptotic normality.

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