Nonparametric estimation in fractional SDE

Fabienne Comte () and Nicolas Marie ()
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Fabienne Comte: Université Paris Descartes
Nicolas Marie: Université Paris Nanterre

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 2, 359-382

Abstract: 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.

Keywords: Stochastic differential equations; Fractional Brownian motion; Nadaraya-Watson estimator; Malliavin calculus; Long-time behavior; Fractional Ornstein-Uhlenbeck process (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11203-019-09196-y

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