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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03189177
Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Wednesday, September 8, 2021 - 11:03:57 PM
Last modification on : Thursday, October 21, 2021 - 3:16:06 PM

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• HAL Id : hal-03189177, version 2

### Citation

Nicolas Marie. Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion. Statistics and Probability Letters, Elsevier, 2022, 180. ⟨hal-03189177v2⟩

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