Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities: polynomially growing drift coefficients and discontinuous drift coefficients. For SDEs that suffer from both irregularities we prove strong convergence of order $1/2$ of the tamed-Euler-Maruyama scheme from [Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012].

翻译：文献中对不规则系数的随机微分方程数值方法有深入研究，各类不规则性通常被分别处理。本文综合研究了两种不同类型的不规则性：多项式增长漂移系数与不连续漂移系数。针对同时存在这两种不规则性的随机微分方程，我们证明了文献[Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012]提出的驯化欧拉-丸山格式具有$1/2$阶强收敛性。