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A class of Hamiltonian stochastic differential equations with multiplicativeL\'{e}vy noise in the sense of Marcus, and the construction and numericalimplementation methods of symplectic Euler scheme, are considered. A generalsymplectic Euler scheme for this kind of Hamiltonian stochastic differentialequations is devised, and its convergence theorem is proved. The second partpresents realizable numerical implementation methods for this scheme indetails. Some numerical experiments are conducted to demonstrate theeffectiveness and superiority of the proposed method by the simulations of itsorbits, Hamlitonian,and convergence order over a long time interval.

Symplectic method for Hamiltonian stochastic differential equations with multiplicative L\'{e}vy noise in the sense of Marcus