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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Comte, F., Marie, N. Nonparametric estimation in fractional SDE. Stat Inference Stoch Process 22, 359–382 (2019). https://doi.org/10.1007/s11203-019-09196-y
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DOI: https://doi.org/10.1007/s11203-019-09196-y