Nonparametric estimation for I.I.D. paths of fractional SDE

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

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 3, No 6, 669-705

Abstract: Abstract This paper deals with nonparametric estimators of the drift function b computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian motion (fSDE). First, a risk bound is established on a Skorokhod’s integral based least squares oracle $${\widehat{b}}$$ b ^ of b. Thanks to the relationship between the solution of the fSDE and its derivative with respect to the initial condition, a risk bound is deduced on a calculable approximation of $${\widehat{b}}$$ b ^ . Another bound is directly established on an estimator of $$b'$$ b ′ for comparison. The consistency and rates of convergence are established for these estimators in the case of the compactly supported trigonometric basis or the $${\mathbb {R}}$$ R -supported Hermite basis.

Keywords: Fractional Brownian motion; Nonparametric projection estimator; Stochastic differential equation; 62M09; 62G08; 60G22; 60H07 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11203-021-09246-4

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