This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a blowup of moments of solutions and numerical solutions and thus affect the convergence of numerical methods. Wang et al. (2023, IMA J. Numer. Anal.) have analyzed weak convergence of one-step numerical schemes when solutions to SDEs have all finite moments. Therein some modified Euler schemes have been discussed about their weak convergence orders. In this work, we explore the effects of limited orders of moments on the weak convergence of a family of explicit schemes. The schemes are based on approximations/modifications of terms in the Ito-Talyor expansion. We provide a systematic but simple way to establish weak convergence orders for these schemes. We present several numerical examples of these schemes and show their weak convergence orders.

翻译：本文是关于求解具有单边Lipschitz条件的随机微分方程（SDEs）一步格式弱收敛性系列研究的第二篇。已知超线性系数可能导致精确解与数值解的矩发生爆破，从而影响数值方法的收敛性。Wang等人（2023, IMA J. Numer. Anal.）在SDE解具有所有有限矩的条件下，分析了一步数值格式的弱收敛性，其中讨论了一些修正欧拉格式的弱收敛阶。在本工作中，我们探讨了有限矩阶数对一类显式格式弱收敛性的影响。这些格式基于对伊藤-泰勒展开式中各项的逼近/修正。我们提供了一种系统而简洁的方法来建立这些格式的弱收敛阶。我们给出了这些格式的若干数值算例，并展示了其弱收敛阶。