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.

- O.Bencheikh, B. Jourdain.
*Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean*ESAIM: PROCEEDINGS AND SURVEYS, Vol.65, p. 219-235,2019.

- Perturbation Techniques in Stochastic Analysis and Its Applications (CIRM), Marseille, France, 11/03/19-15/03/19
- Semaine d'études Maths-Entreprises (SEME), Orsay, France, 14/01/19-18/01/19
- 11th European Summer School in Financial Mathematics, Paris, France, 27/08-31/08/2018
- Groupe de Travail Méthodes Stochastiques et Finance - CERMICS, 14/06/2018
- Journée des Doctorants, Université Paris-Est, 04/06/2018
- Young Researchers Seminar - CERMICS, 22/05/2018

- Statistiques numériques et analyse de données, 2A Ecole des Ponts ParisTech (Lectures & Tutorials)
- Décision dans l'incertain, 1A Ecole des Ponts ParisTech (Tutorials)

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.

Oumaima Bencheikh

CERMICS, École Nationale des Ponts et Chaussées

6 et 8, av. Blaise Pascal

Cité Descartes - Champs-sur-Marne

77455 Marne-la-Vallée cedex 2

France

E-mail: oumaima[dot]bencheikh[at]enpc[dot]fr