Charles-Edouard Bréhier

Publications

Article dans une revue (52)

Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation Charles-Edouard Bréhier,Jianbo Cui,Xiaojie Wang Communications in Mathematical Sciences, 2026, 24 (2), pp.521-564. ⟨10.4310/CMS.260103023620⟩ Article dans une revue hal-03727797v1
Weak error estimates of Galerkin approximations for the stochastic Burgers equation driven by additive trace-class noise Charles-Edouard Bréhier,Sonja Cox,Annie Millet Potential Analysis, 2026, 64 (2), pp.35. ⟨10.1007/s11118-025-10272-7⟩ Article dans une revue hal-04856373v1
Stochastic conformal integrators for linearly damped stochastic poisson systems Charles-Édouard Bréhier,David Cohen,Yoshio Komori Journal of Scientific Computing, 2025, 106 (1), pp.17. ⟨10.1007/s10915-025-03097-4⟩ Article dans une revue hal-04975253v1
Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: Applications to fluid turbulence and generation of fractional Gaussian fields Geoffrey Beck,Charles-Edouard Bréhier,Laurent Chevillard,Ricardo Grande,Wandrille Ruffenach Physical Review Research, 2024, 6 (3), pp.033048. ⟨10.1103/PhysRevResearch.6.033048⟩ Article dans une revue hal-04651190v1
Analysis of a Modified Regularity-Preserving Euler Scheme for Parabolic Semilinear SPDEs: Total Variation Error Bounds for the Numerical Approximation of the Invariant Distribution Charles-Édouard Bréhier Foundations of Computational Mathematics, 2024, ⟨10.1007/s10208-024-09644-z⟩ Article dans une revue hal-04950021v1
Total Variation Error Bounds for the Approximation of the Invariant Distribution of Parabolic Semilinear SPDEs Using the Standard Euler Scheme Charles-Édouard Bréhier Potential Analysis, 2024, 62 (1), pp.101-136. ⟨10.1007/s11118-024-10132-w⟩ Article dans une revue hal-04950029v1
Splitting integrators for linear Vlasov equations with stochastic perturbations Charles-Édouard Bréhier,David Cohen Journal of Computational Dynamics, 2024, 11 (4), pp.494-532. ⟨10.3934/jcd.2024014⟩ Article dans une revue hal-04950035v1
Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime Charles-Edouard Bréhier Journal of Computational Dynamics, 2024, 11 (2), pp.189-219. ⟨10.3934/jcd.2024009⟩ Article dans une revue hal-03741112v1
Numerical Approximation of the Invariant Distribution for a Class of Stochastic Damped Wave Equations Ziyi Lei,Charles-Édouard Bréhier,Siqing Gan Journal of Computational Mathematics -International Edition-, 2024, ⟨10.4208/jcm.2404-m2023-0144⟩ Article dans une revue hal-04950043v1
Total Variation Error Bounds for the Accelerated Exponential Euler Scheme Approximation of Parabolic Semilinear SPDEs Charles-Édouard Bréhier SIAM Journal on Numerical Analysis, 2024, 62 (3), pp.1171-1190. ⟨10.1137/22M152596X⟩ Article dans une revue hal-04950026v1
Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs Charles-Edouard Bréhier SMAI Journal of Computational Mathematics, 2024, 10, pp.175-228. ⟨10.5802/smai-jcm.110⟩ Article dans une revue hal-03614537v1
General non-linear fragmentation with discontinuous Galerkin methods Maxime Lombart,Charles-Edouard Bréhier,Mark Hutchison,Yueh-Ning Lee Monthly Notices of the Royal Astronomical Society, 2024, 533, pp.4410-4434. ⟨10.1093/mnras/stae2039⟩ Article dans une revue insu-04843505v1
Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations Charles-Edouard Bréhier,David Cohen,Johan Ulander ESAIM: Mathematical Modelling and Numerical Analysis, 2024, 58 (4), pp.1317-1346. ⟨10.1051/m2an/2024032⟩ Article dans une revue hal-04665132v1
Splitting integrators for stochastic Lie--Poisson systems Charles-Edouard Bréhier,David Cohen,Tobias Jahnke Mathematics of Computation, 2023, 92 (343), pp.2167-2216. ⟨10.1090/mcom/3829⟩ Article dans une revue hal-03431169v1
Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski-Kramers diffusion approximation regime Charles-Edouard Bréhier Journal of Computational Dynamics, 2023, 10 (3), pp.387-424. ⟨10.3934/jcd.2023005⟩ Article dans une revue hal-03741115v1
Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations Charles-Edouard Bréhier,David Cohen Applied Numerical Mathematics: an IMACS journal, 2023, 186, pp.57-83. ⟨10.1016/j.apnum.2023.01.002⟩ Article dans une revue hal-02893328v1
Asymptotic behavior of a class of multiple time scales stochastic kinetic equations Charles-Edouard Bréhier,Shmuel Rakotonirina-Ricquebourg Stochastic Processes and their Applications, 2023, 168, pp.104265. ⟨10.1016/j.spa.2023.104265⟩ Article dans une revue hal-03258628v1
Splitting schemes for FitzHugh-Nagumo stochastic partial differential equations Charles-Edouard Bréhier,David Cohen,Giuseppe Giordano Discrete and Continuous Dynamical Systems - Series B, 2023, ⟨10.3934/dcdsb.2023094⟩ Article dans une revue hal-03735693v1
Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme Charles-Edouard Bréhier ESAIM: Probability and Statistics, 2023, ⟨10.1051/ps/2023017⟩ Article dans une revue hal-02955371v1
On asymptotic preserving schemes for a class of stochastic differential equations in averaging and diffusion approximation regimes Charles-Edouard Bréhier,Shmuel Rakotonirina-Ricquebourg Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2022, 20 (1), ⟨10.1137/20M1379836⟩ Article dans une revue hal-02988284v1
Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme Charles-Edouard Bréhier ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (1), pp.151-175. ⟨10.1051/m2an/2021089⟩ Article dans une revue hal-03560973v1
Phoresis in cellular flows: from enhanced dispersion to blockage Romain Volk,Mickaël Bourgoin,Charles-Édouard Bréhier,Florence Raynal Journal of Fluid Mechanics, 2022, 948, pp.A42. ⟨10.1017/jfm.2022.730⟩ Article dans une revue hal-03619951v2
Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion Charles-Edouard Bréhier,David Cohen SIAM/ASA Journal on Uncertainty Quantification, 2022, 10 (1), ⟨10.1137/20M1378168⟩ Article dans une revue hal-02986230v1
The averaging principle for stochastic differential equations driven by a Wiener process revisited Charles-Edouard Bréhier Comptes Rendus. Mathématique, 2022, 360, pp.265-273. ⟨10.5802/crmath.297⟩ Article dans une revue hal-03211903v1
Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime Charles-Edouard Bréhier Journal of Mathematical Analysis and Applications, 2022, 509 (1), pp.125940. ⟨10.1016/j.jmaa.2021.125940⟩ Article dans une revue hal-03211906v1
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs Assyr Abdulle,Charles-Edouard Bréhier,Gilles Vilmart IMA Journal of Numerical Analysis, 2021, 43 (1), pp.258-292. ⟨10.1093/imanum/drab090⟩ Article dans une revue hal-03133054v1
Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty Elias Ventre,Thibault Espinasse,Charles-Edouard Bréhier,Vincent Calvez,Thomas Lepoutreet al. Journal of Mathematical Biology, 2021, 83 (59), ⟨10.1007/s00285-021-01684-1⟩ Article dans une revue hal-03243421v1
On parareal algorithms for semilinear parabolic Stochastic PDEs Charles-Edouard Bréhier,Xu Wang SIAM Journal on Mathematical Analysis, 2020, ⟨10.1137/19M1251011⟩ Article dans une revue hal-02022432v1
Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs Charles-Edouard Bréhier Journal of Complexity, 2020, ⟨10.1016/j.jco.2019.101424⟩ Article dans une revue hal-01595881v1
Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation Charles-Edouard Bréhier,Ludovic Goudenège BIT Numerical Mathematics, 2020, ⟨10.1007/s10543-019-00788-x⟩ Article dans une revue hal-01764290v2
Analysis of an Adaptive Biasing Force method based on self-interacting dynamics Michel Benaïm,Charles-Edouard Bréhier,Pierre Monmarché Electronic Journal of Probability, 2020, ⟨10.1214/20-EJP490⟩ Article dans une revue hal-02310672v1
On the settling of small grains in dusty discs: analysis and formulas Guillaume Laibe,Charles-Edouard Bréhier,Maxime Lombart Monthly Notices of the Royal Astronomical Society, 2020, ⟨10.1093/mnras/staa994⟩ Article dans une revue hal-03020151v1
On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting Charles-Edouard Bréhier,Tony Lelièvre Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019, 29, pp.033126. ⟨10.1063/1.5081440⟩ Article dans une revue hal-01923385v1
Convergence analysis of adaptive biasing potential methods for diffusion processes Michel Benaïm,Charles-Edouard Bréhier Communications in Mathematical Sciences, 2019, ⟨10.4310/CMS.2019.v17.n1.a4⟩ Article dans une revue hal-01562639v1
Analysis of some splitting schemes for the stochastic Allen-Cahn equation Charles-Edouard Bréhier,Ludovic Goudenège Discrete and Continuous Dynamical Systems - Series B, 2019, ⟨10.3934/dcdsb.2019077⟩ Article dans une revue hal-01688333v1
Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component Charles-Edouard Bréhier Stochastic Processes and their Applications, 2019, ⟨10.1016/j.spa.2019.09.015⟩ Article dans une revue hal-01896026v1
Strong convergence rates of semi-discrete splitting approximations for stochastic Allen–Cahn equation Charles-Edouard Bréhier,Jianbo Cui,Jialin Hong IMA Journal of Numerical Analysis, 2019, ⟨10.1093/imanum/dry052⟩ Article dans une revue hal-01714836v1
Computing return times or return periods with rare event algorithms Thibault Lestang,Francesco Ragone,Charles-Edouard Bréhier,Corentin Herbert,Freddy Bouchet Journal of Statistical Mechanics: Theory and Experiment, 2018, 2018 (4), pp.043213. ⟨10.1088/1742-5468/aab856⟩ Article dans une revue hal-02070403v1
Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient Charles-Edouard Bréhier,Arnaud Debussche Journal de Mathématiques Pures et Appliquées, 2018, 116, pp.193-254. ⟨10.1016/j.matpur.2018.08.010⟩ Article dans une revue hal-01481966v2
Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization Charles-Edouard Bréhier,Martin Hairer,Andrew M Stuart Journal of Computational Mathematics -International Edition-, 2018, ⟨10.4208/jcm.1607-m2016-0539⟩ Article dans une revue hal-01273500v1
Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme Charles-Edouard Bréhier,Marie Kopec IMA Journal of Numerical Analysis, 2017, 37 (3), pp.1. ⟨10.1093/imanum/drw030⟩ Article dans une revue hal-00910323v2
Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting Charles-Edouard Bréhier,Ludovic Goudenège,Loic Tudela Springer Proceedings in Mathematics & Statistics, 2016, Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, 163, pp.245--260. ⟨10.1007/978-3-319-33507-0_10⟩ Article dans une revue hal-01074155v1
High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise Charles-Edouard Bréhier,Gilles Vilmart SIAM Journal on Scientific Computing, 2016, 38 (4), ⟨10.1137/15M1021088⟩ Article dans une revue hal-01153448v2
Convergence of adaptive biasing potential methods for diffusions Michel Benaïm,Charles-Edouard Bréhier Comptes Rendus. Mathématique, 2016, 354 (8), pp.842 - 846. ⟨10.1016/j.crma.2016.05.011⟩ Article dans une revue hal-01294029v1
Unbiasedness of some generalized adaptive multilevel splitting algorithms Charles-Edouard Bréhier,Maxime Gazeau,Ludovic Goudenège,Tony Lelièvre,Mathias Rousset The Annals of Applied Probability, 2016, 26 (6), pp.3559 - 3601. ⟨10.1214/16-AAP1185⟩ Article dans une revue hal-01142704v1
Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme Charles-Edouard Bréhier,Erwan Faou Applied Mathematics Research eXpress, 2015, 2015 (2), pp.167-203. ⟨10.1093/amrx/abv001⟩ Article dans une revue hal-00800133v1
Large deviations principle for the Adaptive Multilevel Splitting Algorithm in an idealized setting Charles-Edouard Bréhier ALEA : Latin American Journal of Probability and Mathematical Statistics, 2015 Article dans une revue hal-01118745v1
Analysis of Adaptive Multilevel Splitting algorithms in an idealized case Charles-Edouard Bréhier,Tony Lelièvre,Mathias Rousset ESAIM: Probability and Statistics, 2015, 19, ⟨10.1051/ps/2014029⟩ Article dans une revue hal-00987297v1
Analysis and simulation of rare events for SPDEs Charles-Edouard Bréhier,Maxime Gazeau,Ludovic Goudenège,Mathias Rousset ESAIM: Proceedings and Surveys, 2015, 48, pp.364-384. ⟨10.1051/proc/201448017⟩ Article dans une revue hal-02746493v1
Approximation of the invariant measure with an Euler scheme for Stochastic PDE's driven by Space-Time White Noise Charles-Edouard Bréhier Potential Analysis, 2014, 40 (1), pp.1-40. ⟨10.1007/s11118-013-9338-9⟩ Article dans une revue hal-00669462v1
Analysis of a HMM time-discretization scheme for a system of Stochastic PDE's Charles-Edouard Bréhier SIAM Journal on Numerical Analysis, 2013, 51 (2), pp.1185-1210. ⟨10.1137/110853078⟩ Article dans une revue hal-00669470v1
Strong and weak order in averaging for SPDEs Charles-Edouard Bréhier Stochastic Processes and their Applications, 2012, 122 (7), pp.2553-2593. ⟨10.1016/j.spa.2012.04.007⟩ Article dans une revue hal-00669457v1

Communication dans un congrès (1)

Transport equation in Fourier and dynamical turbulent fields Geoffrey Beck,Charles-Edouard Bréhier,Laurent Chevillard,Isabelle Gallagher,Ricardo Grandeet al. Waves 2024, 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2024, Berlin, Germany Communication dans un congrès hal-04534268v1

Pré-publication, Document de travail (15)

Error analysis for stochastic gradient optimization schemes using modified equations Charles-Édouard Bréhier,Marc Dambrine,Nassim En-Nebbazi 2026 Pré-publication, Document de travail hal-04773810v2
Strong rate of convergence in the Smoluchowski-Kramers approximation for stochastic partial differential equations Charles-Édouard Bréhier,Ziyi Lei 2026 Pré-publication, Document de travail hal-05552960v1
Analysis of an exponential integrator for stochastic PDEs driven by Riesz noise Charles-Édouard Bréhier,David Cohen,Lluís Quer-Sardanyons,Johan Ulander 2026 Pré-publication, Document de travail hal-05520387v1
Averaging principle for slow-fast fractional stochastic differential equations Charles-Édouard Bréhier,Ibrahima Faye 2025 Pré-publication, Document de travail hal-05297918v1
Preconditioning for the high-order sampling of the invariant distribution of parabolic semilinear SPDEs Charles-Édouard Bréhier,Adrien Busnot Laurent,Arnaud Debussche,Gilles Vilmart 2025 Pré-publication, Document de travail hal-05426627v1
Analysis of splitting schemes for stochastic evolution equations with non-Lipschitz nonlinearities driven by fractional noise Charles-Édouard Bréhier,Xiao-Li Ding,Dehua Wang 2025 Pré-publication, Document de travail hal-05429917v1
Exploring the behavior of asymptotic preserving schemes for a class of stochastic systems Charles-Édouard Bréhier 2025 Pré-publication, Document de travail hal-05287175v1
A causal random synthetic turbulent velocity field: I. The underlying Gaussian structure Matthieu Chatelain,Júlia Domingues Lemos,Wandrille Ruffenach,Mickaël Bourgoin,Charles-Edouard Bréhieret al. 2025 Pré-publication, Document de travail (preprint/prepublication) hal-05268497v1
Modified equations and error analysis for a semi-implicit stochastic optimization scheme Charles-Édouard Bréhier,Marc Dambrine,Nassim En-Nebbazi 2025 Pré-publication, Document de travail hal-04962485v1
A linear model of dynamical sea wavenumber spectra Geoffrey Beck,Charles-Édouard Bréhier,Laurent Chevillard,Ricardo Grande,Wandrille Ruffenach 2025 Pré-publication, Document de travail hal-05005567v3
Positivity-preserving schemes for some nonlinear stochastic PDEs Charles-Edouard Bréhier,David Cohen,Johan Ulander 2023 Pré-publication, Document de travail hal-04077856v1
Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations Charles-Edouard Bréhier,David Cohen,Johan Ulander 2023 Pré-publication, Document de travail hal-04077860v1
Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs Charles-Edouard Bréhier 2022 Pré-publication, Document de travail hal-03614530v1
Analysis and simulation of rare events for SPDE Charles-Edouard Bréhier,Maxime Gazeau,Ludovic Goudenège,Mathias Rousset 2014 Pré-publication, Document de travail hal-00921680v1
A short introduction to Stochastic PDEs Charles-Edouard Bréhier 2014 Pré-publication, Document de travail hal-00973887v2

Thèse (1)

Numerical analysis of highly oscillatory Stochastic PDEs Charles-Edouard Bréhier General Mathematics [math.GM]. École normale supérieure de Cachan - ENS Cachan, 2012. English. ⟨NNT : 2012DENS0068⟩ Thèse tel-00824693v1

HDR (1)

Contributions to stochastic numerics: simulation of infinite dimensional, multiscale and metastable processes Charles-Edouard Bréhier Probability [math.PR]. Université Claude Bernard Lyon 1, 2021 HDR tel-03293156v1

Cours (2)

LECTURE NOTES: INVARIANT DISTRIBUTIONS FOR PARABOLIC SPDEs AND THEIR NUMERICAL APPROXIMATIONS Charles-Edouard Bréhier Doctoral. Invariant distributions for parabolic SPDEs and their numerical approximations, Chinese Academy of Science, Beijing, China, France. 2017 Cours cel-01633504v1
Introduction to numerical methods for Ordinary Differential Equations Charles-Edouard Bréhier Licence. Introduction to numerical methods for Ordinary Differential Equations, Pristina, Kosovo, Serbia. 2016 Cours cel-01484274v1