Symplectic integration for Hamiltonian stochastic differential equations driven by additive L´evy noise

Abstract This paper proposes a general symplectic Euler scheme for a class of Hamiltonian stochastic differential equations driven by L´evy noise in the sense of Marcus form. The convergence of the symplectic Euler scheme for this Hamiltonian stochastic differential equations is investigated. Realizable numerical implementation of this scheme is also provided in details. Numerical experiments are presented to illustrate the effectiveness and superiority of the proposed method by the simulations of its orbits, symplectic structure and Hamiltonian.