We give a unified method to derive the strong convergence rate of the backward Euler scheme for monotone SDEs in $L^p(\Omega)$-norm, with general $p \ge 4$. The results are applied to the backward Euler scheme of SODEs with polynomial growth coefficients. We also generalize the argument to the Galerkin-based backward Euler scheme of SPDEs with polynomial growth coefficients driven by multiplicative trace-class noise.

翻译：我们给出了一种统一的方法来得出单体SDE的落后Euler计划以$L ⁇ p(\Omega)$-norm为单位的强烈趋同率,一般为$p\ge 4 美元。结果适用于具有多元增长系数的落后SODE的落后Euler计划。我们还将这一论点概括化为基于Galerkin的落后Euler计划,由多倍微量级噪音驱动的多倍增长系数的SPDE计划。