Geodesic
On asymptotic behavior of cross-correlogram estimators of response functions in linear Volterra systems
Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 84-98

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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. 
@article{THSP_2009_15_2_a5,
     author = {V. V. Buldygin and I. P. Blazhievska},
     title = {On asymptotic behavior of cross-correlogram estimators of response functions in linear {Volterra} systems},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {84--98},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a5/}
}
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V. V. Buldygin; I. P. Blazhievska. On asymptotic behavior of cross-correlogram estimators of response functions in linear Volterra systems. Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 84-98. http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a5/