We propose a systematic approach to construct a new family of stochastic symplectic schemes for the strong approximation of the solution of stochastic Hamiltonian systems. Our approach is based both on B-series and generating functions. The proposed schemes are a generalization of the implicit midpoint rule, they require derivatives of the Hamiltonian functions of at most order two, and are constructed by defining a generating function. We construct some schemes with strong convergence order one and a half, and we illustrate numerically their long term performance.

中文翻译：

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随机哈密顿系统的一类新辛方法

我们提出了一种系统方法来构造一族新的随机辛格式，以强逼近随机哈密顿系统的解。我们的方法基于 B 级数和生成函数。所提出的方案是隐式中点规则的推广，它们需要最多二阶哈密顿函数的导数，并通过定义生成函数来构造。我们构造了一些具有强收敛阶一半的方案，并用数值说明了它们的长期性能。