Drift-preserving numerical integrators for stochastic Poisson systems. (English) Zbl 1480.65014
Summary: 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.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
Keywords:
stochastic differential equations; stochastic Hamiltonian systems; stochastic Poisson systems; energy; Casimir; trace formula; numerical schemes; strong convergence; weak convergenceReferences:
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