4 papers
Error analysis for stochastic gradient optimization schemes using modified equations
Charles-Edouard Bréhier, Marc Dambrine, Nassim En-Nebbazi
We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time fo…
Averaging principle for slow-fast fractional stochastic differential equations
Charles-Edouard Bréhier, Ibrahima Faye
We prove the averaging principle for a class of stochastic systems. The slow component is solution to a fractional differential equation, which is coupled with a fast component con…
Stochastic conformal integrators for linearly damped stochastic Poisson systems
Charles-Edouard Bréhier, David Cohen, Yoshio Komori
We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: pr…
Weak error estimates of Galerkin approximations for the stochastic Burgers equation driven by additive trace-class noise
Charles-Edouard Bréhier, Sonja Cox, Annie Millet
We establish weak convergence rates for spectral Galerkin approximations of the stochastic viscous Burgers equation driven by additive trace-class noise. Our results complement the…