LMS Journal of Computation and Mathematics

Research Article

Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations

Christopher T. H. Bakera1 and Evelyn Buckwara2

a1 Department of Mathematics, The Victoria University of Manchester, Manchester M13 9PL, cthbaker@maths.man.ac.uk

a2 Department of Mathematics, The Victoria University of Manchester, Manchester M13 9PL, ebuckwar@maths.man.ac.uk

Abstract

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)