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- W3017113886 abstract "On étudie le problème de l'estimation fonctionnelle du coefficient de diffusion, dépendant de la variable d'espace, sous une contrainte de régularité de type Besov et pour une perte Lp. On dispose d'une trajectoire solution discrétisée sur l'intervalle de temps [0, 1]. On montre que sous une condition de minoration du temps local du processus observé, la vitesse minimax est n−sp/(1+2s) comme dans les modèles classiques d'estimation de la densité ou de la régression. On propose un estimateur par ondelettes qui atteint la vitesse optimale. We study the functional estimation of the space dependent diffusion coefficient, for a global Lp-loss over Besov spaces, when the sample path is discretely observed on the time interval [0, 1]. We show that under a suitable assumption on the local time of the diffusion process, the minimax rate of convergence is n−sp/(1+2s) as in classical situations, such as density estimation or nonparametric regression. We propose a wavelet estimator achieving the optimal rate of convergence." @default.
- W3017113886 created "2020-04-24" @default.
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- W3017113886 date "1997-01-01" @default.
- W3017113886 modified "2023-09-26" @default.
- W3017113886 title "Estimation non-paramétrique du coefficient de diffusion pour une perte" @default.
- W3017113886 doi "https://doi.org/10.1016/s0764-4442(97)80186-3" @default.
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