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Scientific Article
unige:41848 
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Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics |
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| Published in | SIAM Journal on Mathematical Analysis. 2015, vol. 53, no. 1, p. 1-16 | |
| Abstract | A new characterization of sufficient conditions for the Lie-Trotter splitting to capture the numerical invariant measure of nonlinear ergodic Langevin dynamics up to an arbitrary order is discussed. Our characterization relies on backward error analysis and needs weaker assumptions than assumed so far in the literature. In particular, neither high weak order of the splitting scheme nor symplecticity are necessary to achieve high order approximation of the invariant measure of the Langevin dynamics. Numerical experiments confirm our theoretical findings. | |
| Keywords | Stochastic differential equations — Splitting method — Langevin dynamics — Weak convergence — Modified differential equations — Backward error analysis — Invariant measure — Ergodicity | |
| Identifiers | DOI: 10.1137/140962644 | |
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| Research group | Analyse numérique | |
| Project | FNS: 200020 144313/1 | |
| Citation (ISO format) | ABDULLE, Assyr, VILMART, Gilles, ZYGALAKIS, Konstantinos C. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. In: SIAM Journal on Mathematical Analysis, 2015, vol. 53, n° 1, p. 1-16. doi: 10.1137/140962644 https://archive-ouverte.unige.ch/unige:41848 |
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