Drift-preserving numerical integrators for stochastic Poisson systems
Artikel i vetenskaplig tidskrift, 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
Författare
David Cohen
Umeå universitet
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Gilles Vilmart
Université de Genève
International Journal of Computer Mathematics
0020-7160 (ISSN) 10290265 (eISSN)
Vol. 99 1 4-20Ämneskategorier
Beräkningsmatematik
Reglerteknik
Signalbehandling
DOI
10.1080/00207160.2021.1922679