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

Serge Cohen (1) , Xavier Guyon (2, 3) , Olivier Perrin (4) , Monique Pontier (1)

1 LSP - Laboratoire de Statistique et Probabilités
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 CES - Centre d'économie de la Sorbonne
4 GREMAQ - Groupe de recherche en économie mathématique et quantitative

In this paper, almost sure convergence and asymptotic normality of generalized quadratic variation are studied. The main result extend classical results of 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 shett and his parameters is also obtained.

Mots clés: Fractional Brownian sheet; identification; estimation of fractional parameter; anisotropy; generalized quadratic variations

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Serge Cohen, Xavier Guyon, Olivier Perrin, Monique Pontier. Singularity functions for fractional processes : application to the fractional Brownian sheet. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2006, 42 (2), pp.187-205. ⟨10.1016/j.anihpb.2005.03.002⟩. ⟨hal-00272022⟩