Charles-Edouard Bréhier

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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
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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

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

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
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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
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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

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

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 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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 Lepoutre et al.

Journal of Mathematical Biology, 2021, 83 (59), ⟨10.1007/s00285-021-01684-1⟩

Article dans une revue hal-03243421v1
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 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
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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
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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
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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
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Transport equation in Fourier and dynamical turbulent fields

Geoffrey Beck , Charles-Edouard Bréhier , Laurent Chevillard , Isabelle Gallagher , Ricardo Grande et al.

Waves 2024, 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2024, Berlin, Germany

Communication dans un congrès hal-04534268v1
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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
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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
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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
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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
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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
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Averaging principle for slow-fast fractional stochastic differential equations

Charles-Édouard Bréhier , Ibrahima Faye

2025

Pré-publication, Document de travail hal-05297918v1
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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 Bréhier et al.

2025

Pré-publication, Document de travail (preprint/prepublication) hal-05268497v1
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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
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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
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Positivity-preserving schemes for some nonlinear stochastic PDEs

Charles-Edouard Bréhier , David Cohen , Johan Ulander

2023

Pré-publication, Document de travail hal-04077856v1
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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
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Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs

Charles-Edouard Bréhier

2022

Pré-publication, Document de travail hal-03614530v1
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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
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A short introduction to Stochastic PDEs

Charles-Edouard Bréhier

2014

Pré-publication, Document de travail hal-00973887v2
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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
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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
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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