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Identification of filtered white noises. (English) Zbl 0932.60037

Summary: A class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener integral, associated with the fractional Brownian motion, is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then, the identification of the first terms of this expansion is used to solve some filtering problems. Futhermore, rates of convergence of the estimators are then given.

MSC:

60G15 Gaussian processes
60G17 Sample path properties
62G05 Nonparametric estimation
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