Communications in Mathematical Sciences
Volume 12 (2014)
Energy-preserving integrators for stochastic Poisson systems
Pages: 1523 – 1539
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