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Institute Henri Poincaré, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2(42), p. 187-205

DOI: 10.1016/j.anihpb.2005.03.002

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Singularity functions for fractional processes : application to the fractional Brownian sheet

Journal article published in 2006 by Serge Cohen, Xavier Guyon, Olivier Perrin, Monique Pontier
This paper is available in a repository.
This paper is available in a repository.

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Abstract

In this paper almost sure convergence and asymptotic normality of generalized quadratic variation are studied. The main result in this paper extend classical results from Baxter and Gladyshev so that they can be applied to fractional Gaussian processes. An application to the estimation of the true axes of a fractional Brownian sheet is also obtained.RésuméOn étudie dans ce papier les propriétés de convergence et de normalité asymptotique des variations quadratiques généralisées d'un champ brownien fractionnaire. Le résultat principal est une extension des résultats classiques de Baxter et Gladyshev au cas de processus gaussiens fractionnaires. Nous appliquons ce résultat à l'estimation de la direction privilégiée de tels processus.