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

04/02/2021

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by   Nicolas Marie, et al.

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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.