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：针对具有超线性增长系数的随机微分方程（SDEs），本文提出了一类单步数值格式弱收敛的误差分析。遵循Milstein关于SDEs单步近似的弱误差分析框架，我们证明了上述SDEs单步离散化的弱收敛一般性结论。作为应用，本文展示了若干半阶强收敛数值格式（如驯化格式和平衡格式）的弱收敛速度。最后通过数值算例验证了理论分析的正确性。