The Weak Euler Scheme for Stochastic Differential Delay Equations

We develop a weak numerical Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The weak Euler scheme has 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