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Article Dans Une Revue Annals of Statistics Année : 2020

Nonparametric drift estimation for i.i.d. paths of stochastic differential equations

Fabienne Comte
Valentine Genon-Catalot
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Résumé

We consider N independent stochastic processes (Xi(t), t ∈ [0, T ]), i = 1,. .. , N , dened by a one-dimensional stochastic dierential equation which are continuously observed throughout a time interval [0, T ] where T is xed. We study nonparametric estimation of the drift function on a given subset A of R. Projection estimators are dened on nite dimensional subsets of L 2 (A, dx). We stress that the set A may be compact or not and the diusion coecient may be bounded or not. A data-driven procedure to select the dimension of the projection space is proposed where the dimension is chosen within a random collection of models. Upper bounds of risks are obtained. March 28, 2019
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Dates et versions

hal-02083474 , version 1 (29-03-2019)

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Citer

Fabienne Comte, Valentine Genon-Catalot. Nonparametric drift estimation for i.i.d. paths of stochastic differential equations. Annals of Statistics, 2020, 48 (6), pp.3336-3365. ⟨10.1214/19-AOS1933⟩. ⟨hal-02083474⟩
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