Drift-preserving numerical integrators for stochastic Poisson systems
Journal article, 2021

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.

strong convergence

stochastic Hamiltonian systems

stochastic Poisson systems

trace formula

energy

numerical schemes

weak convergence

Stochastic differential equations

Casimir

Author

David Cohen

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Umeå University

Gilles Vilmart

University of Geneva

International Journal of Computer Mathematics

0020-7160 (ISSN)

Vol. In Press

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.1080/00207160.2021.1922679

More information

Latest update

6/4/2021 7