All Stories

  1. General non-linear fragmentation with discontinuous Galerkin methods

    Article • Monthly Notices of the Royal Astronomical Society, August 2024, Oxford University Press (OUP)

    Dr Charles-Edouard BREHIER

  2. Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: Applications to fluid turbulence and generation of fractional Gaussian fields

    Article • Physical Review Research, July 2024, American Physical Society (APS)

    Dr Charles-Edouard BREHIER

  3. Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

    Article • ESAIM Mathematical Modelling and Numerical Analysis, July 2024, EDP Sciences

    Dr Charles-Edouard BREHIER

  4. Analysis of a Modified Regularity-Preserving Euler Scheme for Parabolic Semilinear SPDEs: Total Variation Error Bounds for the Numerical Approximation of the Invariant Distribution

    Article • Foundations of Computational Mathematics, February 2024, Springer Science + Business Media

    Dr Charles-Edouard BREHIER

  5. Asymptotic behavior of a class of multiple time scales stochastic kinetic equations

    Article • Stochastic Processes and their Applications, February 2024, Elsevier

    Dr Charles-Edouard BREHIER

  6. Splitting schemes for FitzHugh–Nagumo stochastic partial differential equations

    Article • Discrete and Continuous Dynamical Systems - B, January 2024, American Institute of Mathematical Sciences (AIMS)

    Dr Charles-Edouard BREHIER

  7. Splitting integrators for stochastic Lie–Poisson systems

    Article • Mathematics of Computation, April 2023, American Mathematical Society (AMS)

    Dr Charles-Edouard BREHIER

  8. Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

    Article • Applied Numerical Mathematics, April 2023, Elsevier

    Dr Charles-Edouard BREHIER

  9. Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme

    Article • ESAIM Probability and Statistics, January 2023, EDP Sciences

    Dr Charles-Edouard BREHIER

  10. Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski–Kramers diffusion approximation regime

    Article • Journal of Computational Dynamics, January 2023, American Institute of Mathematical Sciences (AIMS)

    Dr Charles-Edouard BREHIER

  11. Phoresis in cellular flows: from enhanced dispersion to blockage

    Article • Journal of Fluid Mechanics, September 2022, Cambridge University Press

    Dr Charles-Edouard BREHIER

  12. Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime

    Article • Journal of Mathematical Analysis and Applications, May 2022, Elsevier

    Dr Charles-Edouard BREHIER

  13. Strong Rates of Convergence of a Splitting Scheme for Schrödinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion

    Article • SIAM/ASA Journal on Uncertainty Quantification, March 2022, Society for Industrial & Applied Mathematics (SIAM)

    Dr Charles-Edouard BREHIER

  14. On Asymptotic Preserving Schemes for a Class of Stochastic Differential Equations in Averaging and Diffusion Approximation Regimes

    Article • Multiscale Modeling and Simulation, February 2022, Society for Industrial & Applied Mathematics (SIAM)

    Dr Charles-Edouard BREHIER

  15. Reduction of a Stochastic Model of Gene Expression: Lagrangian Dynamics Gives Access to Basins of Attraction as Cell Types and Metastabilty

    Article • September 2020, Cold Spring Harbor Laboratory Press

    Dr Charles-Edouard BREHIER

  16. Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component

    Article • Stochastic Processes and their Applications, June 2020, Elsevier

    Dr Charles-Edouard BREHIER

  17. On the settling of small grains in dusty discs: analysis and formulae

    Article • Monthly Notices of the Royal Astronomical Society, May 2020, Oxford University Press (OUP)

    Dr Charles-Edouard BREHIER

  18. Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs

    Article • Journal of Complexity, February 2020, Elsevier

    Dr Charles-Edouard BREHIER

  19. On Parareal Algorithms for Semilinear Parabolic Stochastic PDEs

    Article • SIAM Journal on Numerical Analysis, January 2020, Society for Industrial & Applied Mathematics (SIAM)

    Dr Charles-Edouard BREHIER

  20. Weak convergence rates of splitting schemes for the stochastic Allen–Cahn equation

    Article • BIT Numerical Mathematics, November 2019, Springer Science + Business Media

    Dr Charles-Edouard BREHIER

  21. On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive multilevel splitting

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, March 2019, American Institute of Physics

    Dr Charles-Edouard BREHIER

  22. Analysis of some splitting schemes for the stochastic Allen-Cahn equation

    Article • Discrete and Continuous Dynamical Systems - B, January 2019, American Institute of Mathematical Sciences (AIMS)

    Dr Charles-Edouard BREHIER

  23. Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient

    Article • Journal de Mathématiques Pures et Appliquées, November 2018, Elsevier

    Dr Charles-Edouard BREHIER

  24. Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

    Article • IMA Journal of Numerical Analysis, July 2018, Oxford University Press (OUP)

    Dr Charles-Edouard BREHIER

  25. Computing return times or return periods with rare event algorithms

    Article • Journal of Statistical Mechanics Theory and Experiment, April 2018, Institute of Physics Publishing

    Dr Charles-Edouard BREHIER

  26. Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization

    Article • Journal of Computational Mathematics, February 2018, Global Science Press

    Dr Charles-Edouard BREHIER

  27. Unbiasedness of some generalized adaptive multilevel splitting algorithms

    Article • The Annals of Applied Probability, December 2016, Institute of Mathematical Statistics

    Dr Charles-Edouard BREHIER

  28. Convergence of adaptive biasing potential methods for diffusions

    Article • Comptes Rendus Mathématique, August 2016, Elsevier

    Dr Charles-Edouard BREHIER

  29. Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme

    Article • IMA Journal of Numerical Analysis, July 2016, Oxford University Press (OUP)

    Dr Charles-Edouard BREHIER

  30. Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting

    Article • January 2016, Springer Science + Business Media

    Dr Charles-Edouard BREHIER

  31. High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise

    Article • SIAM Journal on Scientific Computing, January 2016, Society for Industrial & Applied Mathematics (SIAM)

    Dr Charles-Edouard BREHIER

  32. Recent advances in various fields of numerical probability

    Article • ESAIM Proceedings and Surveys, October 2015, EDP Sciences

    Dr Charles-Edouard BREHIER

  33. Analysis of adaptive multilevel splitting algorithms in an idealized case

    Article • ESAIM Probability and Statistics, January 2015, EDP Sciences

    Dr Charles-Edouard BREHIER

  34. Analysis and simulation of rare events for SPDEs

    Article • ESAIM Proceedings and Surveys, January 2015, EDP Sciences

    Dr Charles-Edouard BREHIER

  35. Analysis of the Monte-Carlo Error in a Hybrid Semi-Lagrangian Scheme

    Article • Applied Mathematics Research eXpress, January 2015, Oxford University Press (OUP)

    Dr Charles-Edouard BREHIER

  36. Approximation of the Invariant Measure with an Euler Scheme for Stochastic PDEs Driven by Space-Time White Noise

    Article • Potential Analysis, March 2013, Springer Science + Business Media

    Dr Charles-Edouard BREHIER

  37. Analysis of an HMM Time-Discretization Scheme for a System of Stochastic PDEs

    Article • SIAM Journal on Numerical Analysis, January 2013, Society for Industrial & Applied Mathematics (SIAM)

    Dr Charles-Edouard BREHIER

  38. Strong and weak orders in averaging for SPDEs

    Article • Stochastic Processes and their Applications, July 2012, Elsevier

    Dr Charles-Edouard BREHIER