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Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics

Zygalakis, Konstantinos C.
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 equationsSplitting methodLangevin dynamicsWeak convergenceModified differential equationsBackward error analysisInvariant measureErgodicity
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Article (Submitted version) (452 Kb) - document accessible for UNIGE members only Limited access to UNIGE
Research group Analyse numérique
Swiss National Science Foundation: 200020 144313/1
(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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Deposited on : 2014-11-14

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