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

Published inFoundations of computational mathematics, vol. 22, no. 3, p. 649-695
Publication date2021-06-07
First online date2021-06-07
Abstract

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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LAURENT, Adrien, VILMART, Gilles. Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds. In: Foundations of computational mathematics, 2021, vol. 22, n° 3, p. 649–695. doi: 10.1007/s10208-021-09495-y
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ISSN of the journal1615-3375
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