Paul-Eric Chaudru de Raynal

ABOUT ME


Since September 2014, I have been a Maître de Conférences at Université Savoie Mont Blanc. I teach at IUT de Chambéry and do my research at LAMA. I was previously (2013-14) ATER at Université de Nice Sophia Antipolis where I completed my PhD thesis (2010-13) under the supervision of Prof. F. Delarue. My researches lie into the connexion between Probability and PDE and also focus on Numerical Probability. As an application, I am especially interested in the well posedness of stochastic system with singular/rough drift and McKean-Vlasov processes as well as their associated particle system interacting in mean field.


Mail: pe dot deraynal at univ-smb.fr


Postal address: LAMA, UMR 5127, Université Savoie Mont Blanc, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France




PRINT AND PREPRINT (by reverse chronological order of the pre-print):



  1. Forward and Backward Stochastic Differential Equations with Normal Constraints in Law

(with Ph. Briand, P. Cardaliaguet and Y. Hu). arXiv, HAL


  1. Schauder estimates for drifted fractional operators in the supercritical case

(with S. Menozzi and E. Priola). arXiv, HAL


  1. Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space

(with N. Frikha). arXiv, HAL


  1. Strong regularization by Brownian noise propagating through weak Hörmander structure

(with I. Honoré and S. Menozzi). arXiv, HAL


  1. Sharp Schauder estimate for some degenerate Kolmogorov equation

(with I. Honoré and S. Menozzi). arXiv, HAL


  1. Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result

(with S. Menozzi). arXiv, HAL


  1. Particles Systems and Numerical Scheme for Mean Reflected Stochastic Differential Equations

(with P. Briand, A. Guillin and C. Labart), arXiv, HAL


  1. Weak regularization by stochastic drift: result and counter-example.

Discrete and Continuous Dynamical Systems (Series A), arXiv, HAL


  1. Strong well-posedness of McKean-Vlasov stochastic differential equation with Hölder drift.

Stochastic Processes and their Applications, arXiv, HAL


  1. A cubature based algorithm to solve McKean-Vlasov forward and decoupled forward-backward stochastic differential equations.

(with C.A. Garcia Trillos). Stochastic Processes and their Applications, arXiv, HAL


  1. Strong existence and uniqueness for stochastic differential equation with Hölder drift and degenerate noise.

Annales de l’Institut Henri Poincaré (B), arXiv, HAL



PROCEEDINGS:



  1. Numerical methods for Stochastic differential equations: two examples

(with G. Pagès and C. Rey). ESAIM : Proc. and Surveys


  1. Recent Advances in various fields of numerical probability

(with C.E. Bréhier, V. Lemaire, F. Panloup and C. Rey). ESAIM : Proc. and Surveys



TECHNICAL REPORT (industrial collaboration):



  1. Asymptotic properties of a deteriorating system under condition-based maintenance and applications.

(with P. Briand, E. Dautrême, E. Idée, C. Labart, W. Lair and E. Remy). HAL, pdf.



THESIS:



  1. Stochastic differential equations : strong well-posedness of singular and degenerate equations; numerical analysis of decoupled forward backward systems of McKean-Vlasov type. PhD Thesis.

(under the supervision of Prof. F. Delarue). HAL.




GRANTS:


in addition to the support of my institute I have received the following supports:


  1. French CNRS delegation (6 month, 02/19-08/19)

  2. ANR IDEX UGA (10,000  2017-2019)