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

By Fabienne Comte, Valentine Genon-Catalot. Annals of Statistics, 2020

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. We consider N independent stochastic processes ( X i ( t ) , t ∈ [0 , T ]) , i = 1 , . . . , N , de(cid:28)ned by a one-dimensional stochastic di(cid:27)erential equation which are continuously observed throughout a time interval [0 , T ] where T is (cid:28)xed. We study nonparametric estimation of the drift function on a given subset A of R . Projection estimators are de(cid:28)ned on (cid:28)nite dimensional subsets of L 2 ( A, dx ) . We stress that the set A may be compact or not and the di(cid:27)usion coe(cid:30)cient 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

Subfields: Control and Systems Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/75091f2ef946419ba9fb63f316087e9788a212d5