Nonparametric estimation in fractional SDE
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.
KeywordsStochastic differential equations Fractional Brownian motion Nadaraya-Watson estimator Malliavin calculus Long-time behavior Fractional Ornstein-Uhlenbeck process
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