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Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2019

Nonparametric Estimation in Fractional SDE

Résumé

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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Dates et versions

hal-01806321 , version 1 (02-06-2018)
hal-01806321 , version 2 (15-01-2019)

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Citer

Fabienne Comte, Nicolas Marie. Nonparametric Estimation in Fractional SDE. Statistical Inference for Stochastic Processes, 2019, 22 (3), pp.359-382. ⟨10.1007/s11203-019-09196-y⟩. ⟨hal-01806321v2⟩
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