Symplectic integration of stochastic Hamiltonian systems is adeveloping branch of stochastic numerical analysis. In the presentpaper, a stochastic generating function approach is proposed, basedon the derivation of stochastic Hamilton-Jacobi PDEs satisfied bythe generating functions, and a method of approximating solutions tothem. Thus, a systematic approach of constructing stochasticsymplectic methods is provided. As validation, numerical tests onseveral stochastic Hamiltonian systems are performed, where some symplectic schemes are constructed via stochastic generatingfunctions. Moreover, generating functions for some known stochasticsymplectic mappings are given.
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Wang et al. (2013) studied this question.
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