Travaux

Preprints (4)

• Averaging principle for slow-fast fractional stochastic differential equations. CEB & Ibrahima Faye. 2025.
  arxiv:2510.04129 , hal-05297918
• A causal random synthetic turbulent velocity field: I. The underlying Gaussian structure. Matthieu Chatelain, Júlia Domingues Lemos, Wandrille Ruffenach, Mickaël Bourgoin, CEB, Laurent Chevillard, Ilias Sibgatullin & Romain Volk. 2025.
  arxiv:2509.12567 , hal-05268497

• Weak error estimates of Galerkin approximations for the stochastic Burgers equation driven by additive trace-class noise. CEB, Sonja Cox & Annie Millet. 2024.
  arxiv:2412.18338 , hal-04856373
• Asymptotic error analysis for stochastic gradient optimization schemes with first and second order modified equations. CEB, Marc Dambrine & Nassim En-Nebbazi. 2024.
  arxiv:2411.05538 , hal-04773810

Articles (49)

• Stochastic conformal integrators for linearly damped stochastic Poisson systems. CEB, David Cohen & Yoshio Komori. 2025+.
  Journal of Scientific Computing (accepted).
• Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation. CEB, Jianbao Cui & Xiaojie Wang. 2025+.
  Communications in Mathematical Sciences (accepted).

• General non-linear fragmentation with discontinuous Galerkin methods. Maxime Lombart, CEB, Mark Hutchison & Yueh-Ning Lee. 2024
  Monthly Notices of the Royal Astronomical Society. DOI: 10.1093/mnras/stae2039
• Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs. CEB. 2024.
  SMAI Journal of Computational Mathematics. DOI : 10.5802/smai-jcm.110
• 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, CEB, Laurent Chevillard, Ricardo Grande & Wandrille Ruffenach. 2024.
  Physical Review Research. DOI : 10.1103/PhysRevResearch.6.033048
• Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations. CEB, David Cohen & Johan Ulander. 2024.
  ESAIM: M2AN. DOI : 10.1051/m2an/2024032
• Numerical approximation of the invariant distribution for a class of stochastic damped wave equations. Ziyi Lei, CEB & Siqing Gan. 2024.
  Journal of Computational Mathematics. DOI : 10.4208/jcm.2404-m2023-0144
• Splitting integrators for linear Vlasov equations with stochastic perturbations. CEB & David Cohen. 2024.
  Journal of Computational Dynamics. DOI : 10.3934/jcd.2024014
• Total variation error bounds for the approximation of the invariant distribution of parabolic semilinear SPDEs using the standard Euler scheme. CEB. 2024.
  Potential Analysis. DOI : 10.1007/s11118-024-10132-w
• Total variation error bounds for the accelerated exponential Euler scheme approximation of parabolic semilinear SPDEs. CEB. 2024.
  Siam Journal on Numerical Analysis. DOI : 10.1137/22M152596X
• Analysis of a modified regularity-preserving Euler scheme for parabolic semilinear SPDEs - total variation error bounds for the numerical approximation of the invariant distribution. CEB. 2024.
  Foundations of Computational Mathematics. DOI : 10.1007/s10208-024-09644-z
• Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong--Zakai diffusion approximation regime. CEB. 2024.
  Journal of Computational Dynamics. DOI : 10.3934/jcd.2024009

• Asymptotic behavior of a class of multiple time scales stochastic kinetic equations. CEB & Shmuel Rakotonirina-Ricquebourg. 2023.
  Stochastic Processes and their Applications. DOI : 10.1016/j.spa.2023.104265
• Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme. CEB. 2023.
  ESAIM: Probability and Statistics. DOI: 10.1051/ps/2023017
• Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski-Kramers diffusion approximation regime. CEB. 2023
  Journal of Computational Dynamics. DOI: 10.3934/jcd.2023005
• Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations. CEB, David Cohen & Giuseppe Giordano. 2023.
  Discrete and Continuous Dynamical Systems - Series B. DOI: 10.3934/dcdsb.2023094
• Splitting integrators for stochastic Lie-Poisson systems. CEB, David Cohen & Tobias Jahnke. 2023.
  Mathematics of Computation. DOI: 10.1090/mcom/3829
• Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations. CEB & David Cohen. 2023.
  Applied Numerical Mathematics. DOI: 10.1016/j.apnum.2023.01.002

• Phoresis in cellular flows: from enhanced dispersion to blockage. Romain Volk, Mickaël Bourgoin, CEB & Florence Raynal. 2022. Communiqué INSIS
  Journal of Fluid Mechanics. DOI: 10.1017/jfm.2022.730
• The averaging principle for stochastic differential equations driven by a Wiener process revisited. CEB. 2022.
  Comptes Rendus de l'Académie des Sciences - Série Mathématique. DOI: 10.5802/crmath.297
• Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion. CEB & David Cohen. 2022.
  SIAM / ASA Journal on Uncertainty Quantification (JUQ). DOI: 10.1137/20M1378168
• On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes. CEB & Shmuel Rakotonirina-Ricquebourg. 2022.
  Siam Multiscale Modeling and Simulation. DOI: 10.1137/20M1379836
• Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme. CEB. 2022.
  ESAIM: M2AN. DOI : 10.1051/m2an/2021089
• Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime. CEB. 2022.
  Journal of Mathematical Analysis and Applications. DOI : 10.1016/j.jmaa.2021.125940

• Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs. Assyr Abdulle, CEB & Gilles Vilmart. 2021.
  IMA Journal of Numerical Analysis. DOI : 10.1093/imanum/drab090
• Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastability. Elias Ventre, Thibault Espinasse, CEB, Vincent Calvez, Thomas Lepoutre & Olivier Gandrillon. 2021.
  Journal of Mathematical Biology. DOI : 10.1007/s00285-021-01684-1

• Analysis of an Adaptive Biasing Force method based on self-interacting dynamics. Michel Benaïm, CEB & Pierre Monmarché. 2020.
  Electronic Journal of Probability. DOI : 10.1214/20-EJP490
• On the settling of small grains in dusty discs: analysis and formulas. Guillaume Laibe, CEB & Maxime Lombart. 2020.
  Monthly Notices of the Royal Astronomical Society. DOI : 10.1093/mnras/staa994
• On parareal algorithms for semilinear parabolic Stochastic PDEs. CEB & Xu Wang. 2020.
  Siam Journal on Numerical Analysis. DOI : 10.1137/19M1251011

• Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation. CEB & Ludovic Goudenège. 2019.
  BIT Numerical Mathematics. DOI : 10.1007/s10543-019-00788-x
• Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component. CEB. 2019.
  Stochastic Processes and their Applications. DOI : 10.1016/j.spa.2019.09.015
• Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs. CEB. 2019.
  Journal of Complexity. DOI : 10.1016/j.jco.2019.101424
• Analysis of some splitting schemes for the stochastic Allen-Cahn equation. CEB & Ludovic Goudenège. 2019.
  Discrete and Continuous Dynamical Systems - Series B (Special issue in honor of Dr. Peter E. Kloeden on the occasion of his 70th birthday). DOI : 10.3934/dcdsb.2019077
• Convergence analysis of Adaptive Biasing Potential methods for diffusion processes. Michel Benaïm & CEB. 2019.
  Communications in Mathematical Sciences. DOI : 10.4310/CMS.2019.v17.n1.a4
• On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting. CEB & Tony Lelièvre. 2019.
  Chaos (Special Issue "Rare Event Sampling Methods: Development, Analysis and Application"). DOI : 10.1063/1.5081440

• Kolmogorov equations and Weak order analysis for SPDEs with nonlinear diffusion coefficient. CEB & Arnaud Debussche. 2018.
  Journal de Mathématiques Pures et Appliquées. DOI : 10.1016/j.matpur.2018.08.010
• Strong convergence rates of semi-discrete splitting approximations for stochastic Allen-Cahn equation. CEB, Jianbao Cui & Jialin Hong. 2018.
  IMA Journal of Numerical Analysis. DOI : 10.1093/imanum/dry052
• Computing return times or return periods with rare event algorithms. Thibault Lestang, Francesco Ragone, CEB, Corentin Herbert & Freddy Bouchet. 2018.
  Journal of Statistical Mechanics: Theory and Experiment. DOI : 10.1088/1742-5468/aab856
• Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization. CEB, Martin Hairer & Andrew Stuart. 2018.
  Journal of Computational Mathematics (Special Issue "Numerics for SPDEs"). DOI : 10.4208/jcm.1607-m2016-0539

• Unbiasedness of some Generalized Adaptive Multilevel Splitting algorithms. CEB, Maxime Gazeau, Ludovic Goudenège, Tony Lelièvre & Mathias Rousset. 2016.
  The Annals of Applied Probability. DOI : 10.1214/16-AAP1185
• High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise. CEB & Gilles Vilmart. 2016.
  Siam Journal of Scientific Computing. DOI : 10.1137/15M1021088
• Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme. CEB & Marie Kopec. 2016.
  IMA Journal of Numerical Analysis. DOI : 10.1093/imanum/drw030
• Convergence of Adaptive Biaising Potential methods for diffusions. Michel Benaïm & CEB. 2016.
  Comptes Rendus de l'Académie des Sciences - Mathématique;. DOI : 10.1016/j.crma.2016.05.011

• Large deviations principle for the Adaptive Multilevel Splitting Algorithm in an idealized setting. CEB. 2015.
  Alea – Latin American Journal of Probability and Mathematical Statistics. Link : alea.impa.br/articles/v12/12-27
• Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme. CEB & Erwan Faou. 2015.
  Applied Mathematics Research Express. DOI : 10.1093/amrx/abv001
• Analysis of Adaptive Multilevel Splitting algorithms in an idealized case. CEB, Tony Lelièvre & Mathias Rousset. 2015.
  ESAIM Probability and Statistics. DOI : 10.1051/ps/2014029

• Approximation of the invariant measure via an Euler scheme for SPDEs driven by space-time white noise. CEB. 2014.
  Potential Analysis. DOI : 10.1007/s11118-013-9338-9

• Analysis of an HMM time-discretization scheme for a system of Stochastic PDEs. CEB. 2013.
  Siam Journal on Numerical Analysis. DOI : 10.1137/110853078

• Strong and Weak orders in Averaging for SPDEs. CEB. 2012.
  Stochastic Processes and their Applications. DOI : 10.1016/j.spa.2012.04.007

Proceedings (8)

• Exploring the behavior of asymptotic preserving schemes for a class of stochastic systems. CEB.
  BIT Numerical Mathematics, special collection celebrating 65 years of BIT numerical mathematics (submitted). hal-05287175
• Recent contributions to stochastic numerics. CEB, Adrien Busnot Laurent, Ludovic Goudenège, Paul Maurer & Urbain Vaes.
  ESAIM: Proceedings and Surveys (Journées MAS 2024) (accepted).
• A linear model of dynamical sea wavenumber spectra. Geoffrey Beck, CEB, Laurent Chevillard, Ricardo Grande & Wandrille Ruffenach.
  Stochastic Transport in Upper Ocean Dynamics proceedings (accepted). hal-05005567
• Modified equations and error analysis for a semi-implicit stochastic optimization scheme. CEB, Marc Dambrine & Nassim En-Nebbazi.
  Seventeenth International Conference Zaragosa-Pau on Mathematics and its Applications/Monografías Matématicas "García De Galdenao", 2024 (accepted) hal-04962485

• Positivity-preserving schemes for some nonlinear stochastic PDEs. CEB, David Cohen & Johan Ulander.
  Sixteenth International Conference Zaragosa-Pau on Mathematics and its Applications/Monografías Matématicas "García De Galdenao", 2022. hal-04077856

• Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting. CEB, Ludovic Goudenège & Loïc Tudela. 2016.
  Monte Carlo and Quasi Monte Carlo Methods 2014. DOI :10.1007/978-3-319-33507-0_10

• Recent advances in various fields of numerical probability. CEB, Paul-Eric Chaudru de Raynal, Vincent Lemaire, Fabien Panloup & Clément Rey. 2015.
  ESAIM: Proceedings and Surveys (Journées MAS 2014). DOI : 10.1051/proc/201551015
• Analysis and simulation of rare events for SPDEs. CEB, Maxime Gazeau, Ludovic Goudenège & Mathias Rousset. 2015.
  ESAIM: Proceedings and Surveys (CEMRACS 2013). DOI : 10.1051/proc/201448017

Unpublished lecture notes

• A short introduction to Stochastic PDEs
  CERMICS-Ecole des Ponts, 2014.
• Invariant distributions for parabolic SPDEs and their numerical approximations
  Forum on Numerical Analysis for SDEs and SPDEs, Beijing, 2017.