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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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03189177
Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Friday, April 2, 2021 - 6:56:05 PM
Last modification on : Thursday, October 21, 2021 - 3:16:06 PM
Long-term archiving on: : Saturday, July 3, 2021 - 6:58:20 PM

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  • HAL Id : hal-03189177, version 1

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Nicolas Marie. Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion. 2021. ⟨hal-03189177v1⟩

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