Structure-Preserving Numerical Methods for Stochastic Poisson Systems

We propose a class of numerical integration methods for stochastic Poisson systems (SPSs) arbitrary dimensions. Based on the Darboux-Lie theorem, we transform SPSs to their canonical form, generalized Hamiltonian (SHSs), via coordinate transformations found by solving certain PDEs defined brackets SPSs. An a-generating function approach with \alpha\in [0,1] is then used create symplectic discretizations SHSs, which are transformed back inverse transformation integrators These proved preserve both structure and Casimir functions Applications three-dimensional rigid body system Lotka-Volterra show efficiency proposed methods.