In this article, we propose a kind of numerical methods based on the Padé approximations, for two kinds of stochastic Hamiltonian systems. For the general
linear stochastic Hamiltonian systems, it is shown that the applied Padé approximations
P(k,k) produce numerical solutions that are symplectic, and the proposed numerical schemes based on
P(r,s) are of root-mean-square convergence order
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linear stochastic Hamiltonian systems with additive noises, the numerical methods using two kinds of Padé approximations,
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linear Hamiltonian systems to the stochastic context.