Drift-preserving numerical integrators for stochastic Poisson systems

05/26/2020

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by   David Cohen, et al.

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We perform a numerical analysis of randomly perturbed Poisson systems. For the considered Itô perturbation of Poisson differential equations, we show the longtime behavior of the energy and quadratic Casimirs for the exact solution. We then propose and analyze 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 one, weak order of convergence two. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.