A variable stepsize implementation for stochastic differential equations

Burrage, Pamela & Burrage, Kevin (2003) A variable stepsize implementation for stochastic differential equations. SIAM Journal on Scientific Computing (SISC), 24(3), pp. 848-864.

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Abstract

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Impact and interest:

30 citations in Scopus
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32 citations in Web of Science®

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ID Code: 57912
Item Type: Journal Article
Refereed: Yes
Keywords: Stochastic differential equations , Runge-Kutta methods , Brownian path
ISSN: 1064-8275
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Stochastic Analysis and Modelling (010406)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 07 Mar 2013 23:19
Last Modified: 15 Apr 2013 02:12

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