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An introduction to numerical methods for stochastic differential equations

Published online by Cambridge University Press:  07 November 2008

Eckhard Platen
Eckhard Platen
Affiliation:
School of Mathematical Sciences and School of Finance and Economics, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia
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Abstract

This paper aims to give an overview and summary of numerical methods for the solution of stochastic differential equations. It covers discrete time strong and weak approximation methods that are suitable for different applications. A range of approaches and results is discussed within a unified framework. On the one hand, these methods can be interpreted as generalizing the well-developed theory on numerical analysis for deterministic ordinary differential equations. On the other hand they highlight the specific stochastic nature of the equations. In some cases these methods lead to completely new and challenging problems.

Type
Research Article
Information
Acta Numerica , Volume 8 , January 1999 , pp. 197 - 246
Copyright
Copyright © Cambridge University Press 1999

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