Singularity functions for fractional processes: application to the fractional Brownian sheet
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 a...
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| Veröffentlicht in: | Annales de l'I.H.P. Probabilités et statistiques 2006-01, Vol.42 (2), p.187-205 |
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| container_title | Annales de l'I.H.P. Probabilités et statistiques |
| container_volume | 42 |
| creator | Cohen, Serge Guyon, Xavier Perrin, Olivier Pontier, Monique |
| description | 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.
On 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. |
| doi_str_mv | 10.1016/j.anihpb.2005.03.002 |
| format | Article |
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| identifier | ISSN: 0246-0203 |
| ispartof | Annales de l'I.H.P. Probabilités et statistiques, 2006-01, Vol.42 (2), p.187-205 |
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| language | eng |
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| source | Alma/SFX Local Collection; NUMDAM |
| subjects | Anisotropy Estimation Exact sciences and technology Fractional Brownian sheet Generalized quadratic variations Mathematics Multivariate analysis Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Statistics Statistics Theory Stochastic processes |
| title | Singularity functions for fractional processes: application to the fractional Brownian sheet |
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