Convergence of the Euler–Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

摘要

We prove strong convergence of order 1/4 - ϵ for arbitrarily small ϵ  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.