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pro vyhledávání: '"Laurent, Adrien"'
Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
Autor:
Bronasco, Eugen, Laurent, Adrien
While backward error analysis does not generalise straightforwardly to the strong and weak approximation of stochastic differential equations, it extends for the sampling of ergodic dynamics. The calculation of the modified equation relies on tedious
Externí odkaz:
http://arxiv.org/abs/2407.07451
Our goal is to highlight some of the deep links between numerical splitting methods and control theory. We consider evolution equations of the form $\dot{x} = f_0(x) + f_1(x)$, where $f_0$ encodes a non-reversible dynamic, so that one is interested i
Externí odkaz:
http://arxiv.org/abs/2407.02127
Autor:
Laurent, Adrien
The aromatic bicomplex is an algebraic tool based on aromatic Butcher trees and used in particular for the explicit description of volume-preserving affine-equivariant numerical integrators. The present work defines new tools inspired from variationa
Externí odkaz:
http://arxiv.org/abs/2307.07984
Autor:
Laurent, Adrien, Munthe-Kaas, Hans
Publikováno v:
Found. Comput. Math. (2024)
The exotic aromatic Butcher series were originally introduced for the calculation of order conditions for the high order numerical integration of ergodic stochastic differential equations in $\mathbb{R}^d$ and on manifolds. We prove in this paper tha
Externí odkaz:
http://arxiv.org/abs/2305.10993
Publikováno v:
Forum of Mathematics Sigma 11 (2023), E69
Aromatic B-series were introduced as an extension of standard Butcher-series for the study of volume-preserving integrators. It was proven with their help that the only volume-preserving B-series method is the exact flow of the differential equation.
Externí odkaz:
http://arxiv.org/abs/2301.10998
Autor:
Laurent, Adrien
Publikováno v:
SIAM J. Sci. Comput. 44 (2022), no. 5, A2895-C398
In molecular dynamics, penalized overdamped Langevin dynamics are used to model the motion of a set of particles that follow constraints up to a parameter $\varepsilon$. The most used schemes for simulating these dynamics are the Euler integrator in
Externí odkaz:
http://arxiv.org/abs/2110.03222
Autor:
Laurent, Adrien, Vilmart, Gilles
Publikováno v:
Found. Comput. Math. 22, 649-695 (2022)
We derive a new methodology for the construction of high order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invari
Externí odkaz:
http://arxiv.org/abs/2006.09743
Autor:
Laurent, Adrien, Vilmart, Gilles
Publikováno v:
SIAM J. Sci. Comput. 42 (2020), no. 1, A115-A139
We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise. Applications include in pa
Externí odkaz:
http://arxiv.org/abs/1902.01716
Akademický článek
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Autor:
Laurent, Adrien, Vilmart, Gilles
Publikováno v:
Math. Comp. 89 (2020), 169-202
We introduce a new algebraic framework based on a modification (called exotic) of aromatic Butcher-series for the systematic study of the accuracy of numerical integrators for the invariant measure of a class of ergodic stochastic differential equati
Externí odkaz:
http://arxiv.org/abs/1707.02877