Convergence of the Euler-Maruyama method for multidimensional SDEs with   discontinuous drift and degenerate diffusion coefficient
  We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve. 
Gunther Leobacher, Michaela Sz\"olgyenyi
math.NA math.PR