55 citations · 139 across the 23 of their papers we have counts for
13 papers · 1 filter
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…
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…
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…
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…
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…
Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization
Charles-Edouard Bréhier, Martin Hairer, Andrew M. Stuart
We consider stochastic semi-linear evolution equations which are driven by additive, spatially correlated, Wiener noise, and in particular consider problems of heat equation (analy…
Large deviations principle for the Adaptive Multilevel Splitting Algorithm in an idealized setting
Charles-Edouard Bréhier
The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile method for the simulation of rare events. It is based on an interacting (via a mutation-selection proc…
Analysis of Adaptive Multilevel Splitting algorithms in an idealized case
Charles-Edouard Bréhier, Tony Lelievre, Mathias Rousset
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile method to estimate rare events probabilities. It is an iterative procedure on an interacting particle s…