Drift-preserving numerical integrators for stochastic Poisson systems
Journal article, 2022
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 Poisson systems
strong convergence
weak convergence
energy
trace formula
Stochastic differential equations
Casimir
stochastic Hamiltonian systems
numerical schemes
Author
David Cohen
Umeå University
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Gilles Vilmart
University of Geneva
International Journal of Computer Mathematics
0020-7160 (ISSN) 10290265 (eISSN)
Vol. 99 1 4-20Subject Categories (SSIF 2011)
Computational Mathematics
Control Engineering
Signal Processing
DOI
10.1080/00207160.2021.1922679