THE WEAK EULER SCHEME FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS

Abstract. We develop a weak numerical Euler scheme for non-linear stochastic delay dierential equations (SDDEs) driven by multidimensional Brownian motion. The weak Euler scheme has order of convergence 1, as in the case of stochastic ordinary dierential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple nite xed delays in the drift and diusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux. 1