Drift-preserving numerical integrators for stochastic Poisson systems
Artikel i vetenskaplig tidskrift, 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

Författare

David Cohen

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Umeå universitet

Gilles Vilmart

Université de Genève

International Journal of Computer Mathematics

0020-7160 (ISSN)

Vol. In Press

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Signalbehandling

DOI

10.1080/00207160.2021.1922679

Mer information

Senast uppdaterat

2021-06-04