Communications in Mathematical Sciences

Volume 12 (2014)

Number 8

Energy-preserving integrators for stochastic Poisson systems

Pages: 1523 – 1539



David Cohen (Matematik och Matematisk Statistik, Umeå universitet, Umeå, Sweden)

Guillaume Dujardin (Inria Lille Nord-Europe and Laboratoire Paul Painlevé UMR, Villeneuve d’Ascq, France)


A new class of energy-preserving numerical schemes for stochastic Hamiltonian systems with non-canonical structure matrix (in the Stratonovich sense) is proposed. These numerical integrators are of mean-square order one and also preserve quadratic Casimir functions. In the deterministic setting, our schemes reduce to methods proposed in [E. Hairer, JNAIAM. J. Numer. Anal. Ind. Appl. Math., 5(1-2), 73–84, 2011] and [D. Cohen, and E. Hairer, BIT, 51(1), 91–101, 2011].


stochastic Poisson systems, Stratonovich SDEs, energy-preserving numerical schemes, stochastic midpoint scheme, Casimir function

2010 Mathematics Subject Classification

60H10, 60H35, 65C20, 65C30

Published 14 May 2014