We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusion coefficient is uniformly elliptic, H\"older continuous and weakly differentiable in the spatial variables while the drift satisfies the Ladyzhenskaya--Prodi--Serrin condition, as considered by Krylov and R\"ockner (2005). In the discrete scheme, the drift is tamed by replacing it by an approximation. A strong rate of convergence of the scheme is provided in terms of the approximation error of the drift in a suitable and possibly very weak topology. A few examples of approximating drifts are discussed in detail. The parameters of the approximating drifts can vary and be fine-tuned to achieve the standard $1/2$-strong convergence rate with a logarithmic factor.

翻译：我们考虑了一种通用的、明确的有色Euler-Maruyama方案,用于使用多种复制性的棕色噪音的多时间性随机差异方程式。扩散系数在空间变量中是均匀的椭圆、H\"老的连续和微小的差异,而漂移满足了Ladyzhenskaya-Prodi-Serrin条件,Krylov和R\'ockner (2005年)认为,在离散的方案中,漂移通过近似来代替它。这个办法的高度趋同率是,在适当和可能非常薄弱的地形学中,漂移近误差是相当高的。详细讨论了近似漂移的几个例子。相近的漂移参数可以不同,并经过微调,以便用对数系数达到标准1/2美元强的趋同率。