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：Translated abstract: 本文针对带有超线性增长系数的随机微分方程（SDEs），对一步数值方案的弱收敛性进行了误差分析。我们基于 Milstein 等人的弱误差分析方法，对上述 SDEs 的一步近似离散化提出了普适性的弱收敛性结论。具体应用方面，我们对若干半阶强收敛的数值方案（例如驯化和平衡方案）进行了弱收敛性率的证明。最后，我们提供一些数值算例以验证理论分析。