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Habilitation à diriger des recherches

Quelques contributions à la contrainte et à la statistique des équations différentielles dirigées par le mouvement brownien fractionnaire ainsi qu’à la sélection de modèle.

Abstract : This thesis deals with results in stochastic analysis and statistics. On the one hand, it presents some results on constrained differential equations driven by the fractional Brownian motion (fDE): an invariance theorem, some fundamental results on the Skorokhod reflection problem defined by a fDE and a Moreau sweeping process (existence, uniqueness and convergence of an approximation scheme of the solution), and the long time behavior of one dimensional fDE with a singular vector field. Two applications in biology are also provided. On the other hand, this thesis presents some results in nonparametric estimation and model selection: consistency and rate of convergence for a Nadaraya-Watson estimator of the drift function of fDE with an additive noise, bandwidth selection for the Wolverton-Wagner estimator and trend estimation of high dimensional multivariate time series.
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Habilitation à diriger des recherches
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Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Friday, November 15, 2019 - 9:25:44 PM
Last modification on : Wednesday, November 3, 2021 - 6:33:29 AM
Long-term archiving on: : Sunday, February 16, 2020 - 12:23:09 PM

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  • HAL Id : tel-02357331, version 1

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Nicolas Marie. Quelques contributions à la contrainte et à la statistique des équations différentielles dirigées par le mouvement brownien fractionnaire ainsi qu’à la sélection de modèle.. Probabilités [math.PR]. Paris X - Nanterre, 2019. ⟨tel-02357331⟩

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