Euler–Maruyama approximations for SDEs with non-Lipschitz coefficients and applications

In this paper Euler–Maruyama approximation for SDE with non-Lipschitz coefficients is proved to converge uniformly to the solution in Lp-space with respect to the time and starting points. As an application, we also study the existence of solution and large deviation principle for anticipative SDE with random initial condition.  2005 Elsevier Inc. All rights reserved.