Paul-Eric Chaudru de Raynal
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):
• Multidimensional stable-driven SDEs with Besov drift
• From the backward Kolmogorov equation on Wasserstein space to propagation of chaos for McKean-Vlasov SDEs
• Forward and Backward Stochastic Differential Equations with Normal Constraints in Law
(with Ph. Briand, P. Cardaliaguet and Y. Hu). arXiv, HAL
• Schauder estimates for drifted fractional operators in the supercritical case
(with S. Menozzi and E. Priola). arXiv, HAL
• Well-posedness for some non-linear diffusion processes and related PDE on the Wasserstein space
• Strong regularization by Brownian noise propagating through weak Hörmander structure
(with I. Honoré and S. Menozzi). arXiv, HAL
• Sharp Schauder estimate for some degenerate Kolmogorov equation
(with I. Honoré and S. Menozzi). arXiv, HAL
• Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result
(with S. Menozzi). (Accepted in) Transaction of the American Mathematical Society, arXiv, HAL
• Particles Systems and Numerical Scheme for Mean Reflected Stochastic Differential Equations
(with P. Briand, A. Guillin and C. Labart), arXiv, HAL
• Weak regularization by stochastic drift: result and counter-example.
Discrete and Continuous Dynamical Systems (Series A), arXiv, HAL
• Strong well-posedness of McKean-Vlasov stochastic differential equation with Hölder drift.
Stochastic Processes and their Applications, arXiv, HAL
• 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
• Strong existence and uniqueness for stochastic differential equation with Hölder drift and degenerate noise.
Annales de l’Institut Henri Poincaré (B), arXiv, HAL
PROCEEDINGS:
• Numerical methods for Stochastic differential equations: two examples
(with G. Pagès and C. Rey). ESAIM : Proc. and Surveys
• 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):
• 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). pdf.
THESIS:
• 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.
SUPPORTS:
in addition to the support of my institute I have received the following supports:
• ANR METANONLIN (hold by J. Tugaut)
• French CNRS delegation (6 month, 02/19-08/19)
• ANR IDEX UGA (10,000 2017-2019)
TEACHING:
• Mathematical basics for IUT Students, DUT 1&2
• Applied Statistics, Master 2