Structure-Preserving Numerical Methods for a Class of Stochastic Poisson Systems

Abstract

We propose a type of numerical methods for a class of stochastic Poisson systems with invariant energy. The proposed numerical methods preserve both the energy and the Casimir functions of the systems. In addition, we provide a new approach of constructing stochastic Poisson integrators which respect the Poisson structure and the Casimir functions of stochastic Poisson systems based on coordinate transformations on the midpoint method. Numerical tests are performed to demonstrate our theoretical analysis.