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A GENERAL DRIFT ESTIMATION PROCEDURE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH ADDITIVE FRACTIONAL NOISE

Abstract : In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is based on the identification of the invariant measure, and we provide consistency results as well as some information about the convergence rate. We also give some examples of coefficients for which the identifiability assumption for the invariant measure is satisfied.
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https://hal.archives-ouvertes.fr/hal-02077420
Contributor : Maylis Varvenne <>
Submitted on : Wednesday, February 26, 2020 - 11:05:29 AM
Last modification on : Monday, March 9, 2020 - 6:16:00 PM

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Fabien Panloup, Samy Tindel, Maylis Varvenne. A GENERAL DRIFT ESTIMATION PROCEDURE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH ADDITIVE FRACTIONAL NOISE. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2020, 14 (1), pp.1075-1136. ⟨10.1214/20-EJS1685⟩. ⟨hal-02077420v2⟩

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