NUMERICAL ANALYSIS OF EXPLICIT ONE-STEP METHODS FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

We consider the problem of strong approximations of the solution of stochastic differential equations of Ito form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler‐ Maruyama scheme.