I am a PhD candidate in Probability at the CERMICS, Ecole des Ponts ParisTech. With my advisor Benjamin Jourdain, we are working on the Acceleration of probabilistic particle methods.
This PhD focuses on the Acceleration of probabilistic particle methods.
Systems of probabilistic particles in mean-field interaction are used in several areas of application: approximation of solutions for non linear PDEs, simulation of rare events, mean-field games ...
The standard simulation technique of a particle system leads to a O(N^2) complexity due to the interaction between the N particles, for a O(N^-1/2 ) precision related to the statistical error. Some acceleration techniques have been developed recently for numerical probabilistic methods in the context of discretization of usual SDEs (MLMC) or backward SDEs (regression and projection). Some attempts to adapt these techniques for models with interaction are emerging.
The goal of this PhD thesis is to compare numerically and theoretically these attempts, and when possible, propose more effective solutions.
I am a former student of the National School of Computer Science and Applied Mathematics of Grenoble (Ensimag) and DEA Lamberton. A detailed resume can be found here.
CERMICS, École Nationale des Ponts et Chaussées
6 et 8, av. Blaise Pascal
Cité Descartes - Champs-sur-Marne
77455 Marne-la-Vallée cedex 2