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46


Journal articles25 documents

  • Charles-Edouard Bréhier. Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2022, 56 (1), pp.151-175. ⟨10.1051/m2an/2021089⟩. ⟨hal-03560973⟩
  • Michel Benaïm, Charles-Edouard Bréhier, Pierre Monmarché. Analysis of an Adaptive Biasing Force method based on self-interacting dynamics. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2020, ⟨10.1214/20-EJP490⟩. ⟨hal-02310672⟩
  • Charles-Edouard Bréhier, Xu Wang. On parareal algorithms for semilinear parabolic Stochastic PDEs. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, ⟨10.1137/19M1251011⟩. ⟨hal-02022432⟩
  • Guillaume Laibe, Charles-Edouard Bréhier, Maxime Lombart. On the settling of small grains in dusty discs: analysis and formulas. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2020, ⟨10.1093/mnras/staa994⟩. ⟨hal-03020151⟩
  • Charles-Edouard Bréhier. Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs. Journal of Complexity, Elsevier, 2020, ⟨10.1016/j.jco.2019.101424⟩. ⟨hal-01595881⟩
  • Charles-Edouard Bréhier, Ludovic Goudenège. Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation. BIT Numerical Mathematics, Springer Verlag, 2020, ⟨10.1007/s10543-019-00788-x⟩. ⟨hal-01764290v2⟩
  • Charles-Edouard Bréhier, Ludovic Goudenège. ANALYSIS OF SOME SPLITTING SCHEMES FOR THE STOCHASTIC ALLEN-CAHN EQUATION. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2019, ⟨10.3934/dcdsb.2019077⟩. ⟨hal-01688333⟩
  • Charles-Edouard Bréhier. Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component. Stochastic Processes and their Applications, Elsevier, 2019, ⟨10.1016/j.spa.2019.09.015⟩. ⟨hal-01896026⟩
  • Charles-Edouard Bréhier, Jianbo Cui, Jialin Hong. Strong convergence rates of semi-discrete splitting approximations for stochastic Allen–Cahn equation. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2019, ⟨10.1093/imanum/dry052⟩. ⟨hal-01714836⟩
  • Michel Benaïm, Charles-Edouard Bréhier. CONVERGENCE ANALYSIS OF ADAPTIVE BIASING POTENTIAL METHODS FOR DIFFUSION PROCESSES. Communications in Mathematical Sciences, International Press, 2019, ⟨10.4310/CMS.2019.v17.n1.a4⟩. ⟨hal-01562639⟩
  • Charles-Edouard Bréhier, Tony Lelièvre. On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting. Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2019, 29, pp.033126. ⟨10.1063/1.5081440⟩. ⟨hal-01923385⟩
  • Thibault Lestang, Francesco Ragone, Charles-Edouard Bréhier, Corentin Herbert, Freddy Bouchet. Computing return times or return periods with rare event algorithms. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2018, 2018 (4), pp.043213. ⟨10.1088/1742-5468/aab856⟩. ⟨hal-02070403⟩
  • Charles-Edouard Bréhier, Martin Hairer, Andrew M Stuart. Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization. Journal of Computational Mathematics -International Edition-, Global Science Press, 2018, ⟨10.4208/jcm.1607-m2016-0539⟩. ⟨hal-01273500⟩
  • Charles-Edouard Bréhier, Arnaud Debussche. Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient. Journal de Mathématiques Pures et Appliquées, Elsevier, 2018, 116, pp.193-254. ⟨10.1016/j.matpur.2018.08.010⟩. ⟨hal-01481966v2⟩
  • Charles-Edouard Bréhier, Marie Kopec. Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2017, 37 (3), pp.1. ⟨10.1093/imanum/drw030⟩. ⟨hal-00910323v2⟩
  • Michel Benaïm, Charles-Edouard Bréhier. Convergence of adaptive biasing potential methods for diffusions. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2016, 354 (8), pp.842 - 846. ⟨10.1016/j.crma.2016.05.011⟩. ⟨hal-01294029⟩
  • Charles-Edouard Bréhier, Gilles Vilmart. High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2016, 38 (4), ⟨10.1137/15M1021088⟩. ⟨hal-01153448v2⟩
  • Charles-Edouard Bréhier, Ludovic Goudenège, Loic Tudela. Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting. Springer Proceedings in Mathematics & Statistics, Springer, 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⟩. ⟨hal-01074155⟩
  • Charles-Edouard Bréhier, Maxime Gazeau, Ludovic Goudenège, Tony Lelièvre, Mathias Rousset. Unbiasedness of some generalized adaptive multilevel splitting algorithms. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2016, 26 (6), pp.3559 - 3601. ⟨10.1214/16-AAP1185⟩. ⟨hal-01142704⟩
  • Charles-Edouard Bréhier, Tony Lelièvre, Mathias Rousset. Analysis of Adaptive Multilevel Splitting algorithms in an idealized case. ESAIM: Probability and Statistics, EDP Sciences, 2015, 19, ⟨10.1051/ps/2014029⟩. ⟨hal-00987297⟩
  • Charles-Edouard Bréhier, Maxime Gazeau, Ludovic Goudenège, Mathias Rousset. Analysis and simulation of rare events for SPDEs. ESAIM: Proceedings and Surveys, EDP Sciences, 2015, 48, pp.364-384. ⟨10.1051/proc/201448017⟩. ⟨hal-02746493⟩
  • Charles-Edouard Bréhier, Erwan Faou. Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme. Applied Mathematics Research eXpress, Oxford University Press (OUP): Policy H - Oxford Open Option A, 2015, 2015 (2), pp.167-203. ⟨10.1093/amrx/abv001⟩. ⟨hal-00800133⟩
  • Charles-Edouard Bréhier. Approximation of the invariant measure with an Euler scheme for Stochastic PDE's driven by Space-Time White Noise. Potential Analysis, Springer Verlag, 2014, 40 (1), pp.1-40. ⟨10.1007/s11118-013-9338-9⟩. ⟨hal-00669462⟩
  • Charles-Edouard Bréhier. Analysis of a HMM time-discretization scheme for a system of Stochastic PDE's. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2013, 51 (2), pp.1185-1210. ⟨10.1137/110853078⟩. ⟨hal-00669470⟩
  • Charles-Edouard Bréhier. Strong and weak order in averaging for SPDEs. Stochastic Processes and their Applications, Elsevier, 2012, 122 (7), pp.2553-2593. ⟨10.1016/j.spa.2012.04.007⟩. ⟨hal-00669457⟩

Preprints, Working Papers, ...18 documents

  • Charles-Edouard Bréhier, Jianbo Cui, Xiaojie Wang. Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation. 2022. ⟨hal-03727797⟩
  • Charles-Edouard Bréhier. Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime. 2022. ⟨hal-03741112⟩
  • Charles-Edouard Bréhier. Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs. 2022. ⟨hal-03614530⟩
  • Charles-Edouard Bréhier. Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski-Kramers diffusion approximation regime. 2022. ⟨hal-03741115⟩
  • Charles-Edouard Bréhier, David Cohen, Giuseppe Giordano. Splitting schemes for FitzHugh-Nagumo stochastic partial differential equations. 2022. ⟨hal-03735693⟩
  • Charles-Edouard Bréhier. Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs. 2022. ⟨hal-03614537⟩
  • Charles-Edouard Bréhier, Shmuel Rakotonirina--Ricquebourg. Asymptotic behavior of a class of multiple time scales stochastic kinetic equations. 2021. ⟨hal-03258628⟩
  • Charles-Edouard Bréhier, David Cohen, Tobias Jahnke. Splitting integrators for stochastic Lie--Poisson systems. 2021. ⟨hal-03431169⟩
  • Charles-Edouard Bréhier. The averaging principle for stochastic differential equations driven by a Wiener process revisited. 2021. ⟨hal-03211903⟩
  • Charles-Edouard Bréhier. Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime. 2021. ⟨hal-03211906⟩
  • Assyr Abdulle, Charles-Edouard Bréhier, Gilles Vilmart. Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs. 2021. ⟨hal-03133054⟩
  • Charles-Edouard Bréhier, David Cohen. STRONG RATES OF CONVERGENCE OF A SPLITTING SCHEME FOR SCHRÖDINGER EQUATIONS WITH NONLOCAL INTERACTION CUBIC NONLINEARITY AND WHITE NOISE DISPERSION. 2020. ⟨hal-02986230⟩
  • Charles-Edouard Bréhier. Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme. 2020. ⟨hal-02955370⟩
  • Charles-Edouard Bréhier. Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme. 2020. ⟨hal-02955371⟩
  • Charles-Edouard Bréhier, David Cohen. ANALYSIS OF A SPLITTING SCHEME FOR A CLASS OF NONLINEAR STOCHASTIC SCHRODINGER EQUATIONS. 2020. ⟨hal-02893328⟩
  • Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg. ON ASYMPTOTIC PRESERVING SCHEMES FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS IN AVERAGING AND DIFFUSION APPROXIMATION REGIMES. 2020. ⟨hal-02988284⟩
  • Charles-Edouard Bréhier. A short introduction to Stochastic PDEs. 2014. ⟨hal-00973887v2⟩
  • Charles-Edouard Bréhier, Maxime Gazeau, Ludovic Goudenège, Mathias Rousset. Analysis and simulation of rare events for SPDE. 2014. ⟨hal-00921680⟩

Habilitation à diriger des recherches1 document

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

Lectures2 documents

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