Scientific article
Open access

Drift-preserving numerical integrators for stochastic Poisson systems

Published inInternational journal of computer mathematics, vol. 99, no. 1, p. 4-20
Publication date2022
First online date2021-05-21

We perform a numerical analysis of a class of randomly perturbed Hamiltonian systems and Poisson systems. For the considered additive noise perturbation of such systems, we show the long-time behaviour of the energy and quadratic Casimirs for the exact solution. We then propose and analyse a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence 1, weak order of convergence 2. These properties are illustrated with numerical experiments.

  • Stochastic differential equations
  • Stochastic Hamiltonian systems
  • Stochastic Poisson systems
  • Energy
  • Casimir
  • Trace formula
  • Numerical schemes
  • Strong convergence
  • Weak convergence
Research group
Citation (ISO format)
COHEN, David, VILMART, Gilles. Drift-preserving numerical integrators for stochastic Poisson systems. In: International journal of computer mathematics, 2022, vol. 99, n° 1, p. 4–20. doi: 10.1080/00207160.2021.1922679
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Article (Published version)
ISSN of the journal0020-7160

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