Nonparametric Estimation for I.I.D. Paths of 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 nonparametric projection estimators of the drift function computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion. A projection least-squares estimator is defined and a $\mathbb L^2$-type risk bound is proved for it. The consistency and rate of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the $\mathbb R$-supported Hermite basis.

Mots clés: Nonparametric projection estimator; Stochastic differential equation; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Fabienne Comte, Nicolas Marie. Nonparametric Estimation for I.I.D. Paths of Fractional SDE. 2020. ⟨hal-02532339v1⟩