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：具有不规则系数的随机微分方程数值方法在文献中得到了深入研究，不同类型的规则性通常被分别处理。在本文中，我们结合了两种不同类型的不规则性：多项式增长漂移系数和不连续漂移系数。对于同时存在这两种不规则性的随机微分方程，我们证明了来自[Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012]的驯化Euler-Maruyama格式具有$1/2$阶强收敛性。