We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein’s weak error analysis on the one-step approximation of SDEs, we prove a general result on weak convergence of the one-step discretization of the SDEs mentioned above. As applications, we show the weak convergence rates for several numerical schemes of half-order strong convergence, such as tamed and balanced schemes. Numerical examples are presented to verify our theoretical analysis.

中文翻译：

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超线性系数SDE强逼近格式的弱误差分析

我们提出了一种对具有超线性增长系数的随机微分方程（SDE）的一步数值格式的弱收敛性的误差分析。继Milstein对SDE的一步逼近的弱误差分析之后，我们证明了上述SDE的一步离散化弱收敛的一般结果。作为应用，我们展示了几种半阶强收敛数值格式的弱收敛率，例如驯服格式和平衡格式。给出了数值例子来验证我们的理论分析。