Research

Thesis in statistics defended on december the 12th 2023

Subject : Supervised classification and nonparametric estimation for SDEs.

My research focuses on the construction of classification procedures for functional data modeled by diffusion processes. Since one of the proposed procedure follows the plug-in principle, the thesis also focuses on statictical inference of coefficients of stochastic differential equations.  

My research interests are at the intersection of theoritical statistics (parametric and non-parametric estimation, regression), stochastic calculus (stochastic differential equations, diffusion processes) and machine learning (supervised learning on different types of data). 

In the framework of my thesis, the construction of classification methods is based on the explotation of proprieties of solutions of time-homogeneous and in-homogeneous stochastic differential equations.

This thesis was supervised by Christophe Denis (LAMA, Gustave Eiffel University), Charlotte Dion-Blanc (LPSM, Sorbonne University), Viet-Chi Tran (LAMA, Gustave Eiffel University). 

Key words : diffusion processes, non-parametric estimation, supervised classification of paths, empirical risk minimization, implementation in R and python.

Targeted expertise : Statistical learning, Stochastic calculus, high-dimensional statistics, process statistics.