| Abstract: | The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general, the proposed symplectic schemes are fully implicit, and they become computationally
expensive for mean square orders greater than two. However, for stochastic Hamiltonian systems preserving Hamiltonian functions, the high-order symplectic methods
have simpler forms than the explicit Taylor expansion schemes. A theoretical analysis
of the convergence and numerical simulations are reported for several symplectic integrators. The numerical case studies confirm that the symplectic methods are efficient
computational tools for long-term simulations. |
