| Abstract: |
| Stochastic Poisson systems generalize stochastic Hamiltonian systems in dimension and structural matrices. In this talk we introduce some recent study on structure-preserving numerical methods for stochastic Poisson systems, including the approach of Darboux-Lie transformations, the midpoint-related methods, and the projection-based methods that can simultaneously preserve all invariant Hamiltonians. These methods are constructed to inherit the Poisson structure, the Casimir functions, or the invariant energy (resp. Hamiltonians) of the stochastic Poisson systems. Numerical tests are performed on some typical examples including the stochastically perturbed rigid body system and Lotka-Volterra system. |
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