This article is cited in 2 papers

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

V. V. Buldygin, I. P. Blazhievska

National Technical University of Ukraine "KPI", Department of Higher Mathematics No 1, Pr. Peremohy 37, 02056 Kiev, Ukraine

Abstract: 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.

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

MSC: Primary 62M10; Secondary 60F17

Language: English

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