Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds
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AbstractWe 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.
2021 ◽
Vol 0
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pp. 0
Keyword(s):
2006 ◽
Vol 24
(1)
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pp. 97-134
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STOCHASTIC DIFFERENTIAL EQUATIONS ON MANIFOLDS (London Mathematical Society Lecture Note Series, 70)
1984 ◽
Vol 16
(2)
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pp. 189-191