a1 Department of Mathematics, The Victoria University of Manchester, Manchester M13 9PL, email@example.com
a2 Department of Mathematics, The Victoria University of Manchester, Manchester M13 9PL, firstname.lastname@example.org
We consider the problem of strong approximations of the solution of stochastic differential equations of Itô 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.
(Received January 18 2000)
(Revised October 11 2000)
(Accepted November 24 2000)