We study weak convergence of an Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.
Buckwar, Evelyn, Kuske, Rachel, Mohammed, Salah-Eldin A. and Shardlow, Tony. "The Weak Euler Scheme for Stochastic Delay Equations." (May 2008).