We show that applying any deterministic B-series method of order pd with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order left perpendicular pd/2 right perpendicular. As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.

中文翻译：

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单被积函数 Stratonovich SDE 的高阶数值积分器

我们表明，将具有随机步长的 pd 阶的任何确定性 B 系列方法应用于单个被积函数 SDE 会给出一种数值方法，该方法在均方和弱意义上收敛，阶左垂直 pd/2 右垂直。作为一个应用，我们推导出了随机泊松系统的高阶能量守恒方法以及这类 Stratonovich SDE 的进一步几何数值方案。