Abstract
We consider the identification of the relevant parameters of the symbol of the pseudo-differential operator defining an Elliptic Gaussian Random Process. This identification is done by using the observation of the discretization of one sample path of the process. Constructive estimators based on generalization of quadratic variations are given. Almost sure convergence of these estimators is proved.
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Benassi, A., Jaffard, S., Roux, D. (1994a): Gaussian processes and Pseudodif-ferential Elliptic operators. To appear in Revista Mathematica Iberoamericana.
Benassi, A., Cohen, S., Jaffard, S. (1994b): Identification de processus gaussiens elliptiques. Cr. Acad. Sc. Paris, Série I. 319, 877–880.
Benassi, A., Cohen, S., Istas, J., Jaffard, S. (Preprint 1996): Identification of Filtered White Noises.
Ezzine, A. (1996): Méthodes d’ondelettes pour la résolution numérique d’equations intégrales (Thèse de l’Ecole Nationale des Ponts et Chaussées). To appear.
Istas, J. (1996): Estimating the singularity function of a Gaussian process with applications. Scand. J. Statist. Vol. 23, 5, 1996, 581–596.
Istas, J., Lang, G. (1997): Quadratic variations and estimation of the local Holder index of a Gaussian process. Ann. Inst. H. Poincaré. To appear.
Mandelbrot, B., Van Ness, J. (1968): Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review. 10, 422–437.
Meyer, Y. (1990): Ondelettes et Opérateurs. volume 1. Hermann, Paris.
Meyer, Y. (1990): Ondelettes et Opérateurs. volume 2. Hermann, Paris.
Pentland, A. (1984): Fractal-based description of natural scenes. IEEE Trans., PAMI, 6, 661–674.
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© 1997 Springer-Verlag London Limited
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Benassi, A., Cohen, S., Istas, J., Jaffard, S. (1997). Identification of Elliptic Gaussian Random Processes. In: Lévy Véhel, J., Lutton, E., Tricot, C. (eds) Fractals in Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0995-2_10
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DOI: https://doi.org/10.1007/978-1-4471-0995-2_10
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