Nonparametric Estimation for I.I.D. Paths of Fractional SDE

04/04/2020

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by   Fabienne Comte, et al.

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Université Paris Descartes

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Paris Nanterre University

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This paper deals with nonparametric projection estimators of the drift function computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion. A projection least-squares estimator is defined and a L^2-type risk bound is proved for it. The consistency and rate of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the R-supported Hermite basis.