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 conclusion 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.

翻译：本文针对具有超线性增长系数的随机微分方程（SDEs）单步数值格式的弱收敛性进行误差分析。基于Milstein关于SDE单步近似的弱误差分析理论，我们证明了上述SDE单步离散格式弱收敛的一个一般性结论。作为应用，我们展示了若干具有半阶强收敛性的数值格式（如驯服格式与平衡格式）的弱收敛速率。通过数值算例验证了理论分析结果。