Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion

Nicolas Marie (1)

1 MODAL'X - Modélisation aléatoire de Paris X

The paper deals with projection estimators of the density of the stationary solution $X$ to a differential equation driven by the fractional Brownian motion under a dissipativity condition on the drift function. A model selection method is provided and, thanks to the concentration inequality for Lipschitz functionals of discrete samples of $X$ proved in Bertin et al. (2020), an oracle inequality is established for the adaptive estimator.

Domaines: Statistiques [math.ST]

Nicolas Marie. Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion. Statistics and Probability Letters, 2022, 180, 9 p. ⟨10.1016/j.spl.2021.109244⟩. ⟨hal-03189177v2⟩