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Nonparametric Estimation in Fractional SDE

Abstract : This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fractional noise. The results of this paper are obtained via both some long-time behavior properties of Hairer and some properties of the Skorokhod integral with respect to the fractional Brownian motion. These results are illustrated on the fractional Ornstein-Uhlenbeck process.
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Submitted on : Tuesday, January 15, 2019 - 1:09:28 PM
Last modification on : Thursday, October 21, 2021 - 3:16:06 PM
Long-term archiving on: : Tuesday, April 16, 2019 - 2:44:57 PM


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Fabienne Comte, Nicolas Marie. Nonparametric Estimation in Fractional SDE. Statistical Inference for Stochastic Processes, Springer Verlag, 2019, ⟨10.1007/s11203-019-09196-y⟩. ⟨hal-01806321v2⟩



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