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

Published online by Cambridge University Press:  01 February 2010

Christopher T. H. Baker  and
Evelyn Buckwar
Christopher T. H. Baker
Affiliation:
Department of Mathematics, The Victoria University of Manchester, Manchester M13 9PL, cthbaker@maths.man.ac.uk
Evelyn Buckwar
Affiliation:
Department of Mathematics, The Victoria University of Manchester, Manchester M13 9PL, ebuckwar@maths.man.ac.uk

Abstract

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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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000 , pp. 315 - 335
Copyright
Copyright © London Mathematical Society 2000

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