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Article Dans Une Revue Foundations of Computational Mathematics Année : 2022

Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

Résumé

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 invariant measure for a class of Runge???Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.
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hal-04347690 , version 1 (15-12-2023)

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Adrien Laurent, Gilles Vilmart. Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds. Foundations of Computational Mathematics, 2022, 22, pp.649-695. ⟨10.1007/s10208-021-09495-y⟩. ⟨hal-04347690⟩
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