Weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with non-regular drift

摘要

We consider an Euler–Maruyama type approximation method for a stochastic differential equation (SDE) with a non-regular drift and regular diffusion coefficient. The method regularizes the drift coefficient within a certain class of functions and then the Euler–Maruyama scheme for the regularized scheme is used as an approximation. This methodology gives two errors. The first one is the error of regularization of the drift coefficient within a given class of parametrized functions. The second one is the error of the regularized Euler–Maruyama scheme. After an optimization procedure with respect to the parameters we obtain various rates, which improve other known results.