6 papers · 1 filter
Post-processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
Adrien Busnot Laurent, Sébastien Macé
In this work, we propose a novel intrinsic approach to the approximation of ergodic SDEs on Riemannian manifolds, which include Riemannian Langevin dynamics. In opposition to the s…
Control theory and splitting methods
Karine Beauchard, Adrien Busnot Laurent, Frédéric Marbach
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form , wher…
Derivation of optimal stochastic Runge-Kutta methods with exotic and decorated Butcher series for the weak integration of stochastic dynamics
Adrien Busnot Laurent, Kristian Debrabant, Anne Kværnø
The design of numerical integrators for solving stochastic dynamics with high weak order relies on tedious calculations and is subject to a high number of order conditions. The ori…
Preconditioning for the high-order sampling of the invariant distribution of parabolic semilinear SPDEs
Charles-Edouard Bréhier, Adrien Busnot Laurent, Arnaud Debussche +1
For a class of ergodic parabolic semilinear stochastic partial differential equations (SPDEs) with gradient structure, we introduce a preconditioning technique and design high-orde…
High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods
Eugen Bronasco, Adrien Busnot Laurent, Baptiste Huguet
We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In o…
Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
Eugen Bronasco, Adrien Laurent
While backward error analysis does not generalise straightforwardly to the strong and weak approximation of stochastic differential equations, it extends for the sampling of ergodi…