55 citations · 139 across the 23 of their papers we have counts for
31 papers
Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation
Charles-Edouard Bréhier, Jianbo Cui, Xiaojie Wang
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise.…
Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs
Charles-Edouard Bréhier
We study an asymptotic preserving scheme for the temporal discretization of a system of parabolic semilinear SPDEs with two time scales. Owing to the averaging principle, when the…
Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs
Charles-Edouard Bréhier
We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white no…
Splitting integrators for stochastic Lie--Poisson systems
Charles-Edouard Bréhier, David Cohen, Tobias Jahnke
We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisso…
Asymptotic behavior of a class of multiple time scales stochastic kinetic equations
Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters and : the evolution equation contains singular terms with respect to $…
Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime
Charles-Edouard Bréhier
We design numerical schemes for a class of slow-fast systems of stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and the slow component…
The averaging principle for stochastic differential equations driven by a Wiener process revisited
Charles-Edouard Bréhier
We consider a one-dimensional stochastic differential equation driven by a Wiener process, where the diffusion coefficient depends on an ergodic fast process. The averaging princip…
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs
Assyr Abdulle, Charles-Edouard Bréhier, Gilles Vilmart
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators ap…
On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes
Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg
We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some exampl…
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
We analyse a splitting integrator for the time discretization of the Schrödinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that thi…
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
We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz c…
Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme
Charles-Edouard Bréhier
We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by addi…
Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations
Charles-Edouard Bréhier, David Cohen
We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive Itô noise. The…
Analysis of an Adaptive Biasing Force method based on self-interacting dynamics
Michel Benaïm, Charles-Edouard Bréhier, Pierre Monmarché
This article fills a gap in the mathematical analysis of Adaptive Biasing algorithms, which are extensively used in molecular dynamics computations. Given a reaction coordinate, id…
On parareal algorithms for semilinear parabolic Stochastic PDEs
Charles-Edouard Bréhier, Xu Wang
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes,…
Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component
Charles-Edouard Bréhier
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle…
Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation
Charles-Edouard Bréhier, Ludovic Goudenège
This article is devoted to the analysis of the weak rates of convergence of schemes introduced by the authors in a recent work, for the temporal discretization of the stochastic Al…
Strong convergence rates of semi-discrete splitting approximations for stochastic Allen--Cahn equation
Charles-Edouard Bréhier, Jianbo Cui, Jialin Hong
This article analyzes an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise, in a bounded spatial domain with smooth bound…
Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation
Charles-Edouard Bréhier, Ludovic Goudenège
We introduce and analyze an explicit time discretization scheme for the one-dimensional stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting…
Computing return times or return periods with rare event algorithms
Thibault Lestang, Francesco Ragone, Charles-Edouard Bréhier +2
The average time between two occurrences of the same event, referred to as its return time (or return period), is a useful statistical concept for practical applications. For insta…
Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs
Charles-Edouard Bréhier
This article investigates the role of the regularity of the test function when considering the weak error for standard discretizations of SPDEs of the form $dX(t)=AX(t)dt+F(X(t))dt…
Convergence analysis of Adaptive Biasing Potential methods for diffusion processes
Michel Benaïm, Charles-Edouard Bréhier
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adapti…
Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient
Charles-Edouard Bréhier, Arnaud Debussche
We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This gene…
Convergence of Adaptive Biasing Potential methods for diffusions
Michel Benaïm, Charles-Edouard Bréhier
We prove the consistency of an adaptive importance sampling strategy based on biasing the potential energy function of a diffusion process ; for…