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arXiv · 2104.01144

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

Nicolas Marie
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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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Nicolas Marie. 2021-04-02. Projection Estimators of the Stationary Density of a Differential Equation Driven by the Fractional Brownian Motion. https://doi.org/10.1016/j.spl.2021.109244

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