Weak approximation of stochastic differential delay equations

A numerical method for a class of Itô stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parameterised by its time step. Weak convergence with respect to a class of smooth test functionals is established by using the infinite dimensional version of the Kolmogorov equation. With regularity assumptions on coefficients and initial data, the rate of convergence is shown to be proportional to the time step. Some computations are presented to demonstrate the rate of convergence.