Nonparametric Estimation in Fractional SDE

Fabienne Comte (1) , Nicolas Marie (2, 3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 MODAL'X - Modélisation aléatoire de Paris X
3 ESME - ESME - École spéciale de mécanique et d'électricité

This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via both some long-time behavior properties of Hairer and some properties of the Skorokhod integral with respect to the fractional Brownian motion. These results are illustrated on the fractional Ornstein-Uhlenbeck process.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Fabienne Comte, Nicolas Marie. Nonparametric Estimation in Fractional SDE. 2018. ⟨hal-01806321v1⟩