Order conditions of stochastic Runge-Kutta methods by B-series

Burrage, Kevin & Burrage, Pamela (2000) Order conditions of stochastic Runge-Kutta methods by B-series. SIAM Journal on Numerical Analysis, 38(5), pp. 1626-1646.

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Abstract

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

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63 citations in Web of Science®

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ID Code: 57772
Item Type: Journal Article
Refereed: Yes
Keywords: Runge-Kutta Methods, Stochastic differential equations
DOI: 10.1137/S0036142999363206
ISSN: 0036-1429
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Stochastic Analysis and Modelling (010406)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2000 Society for Industrial and Applied Mathematics
Deposited On: 05 Mar 2013 00:39
Last Modified: 12 Apr 2013 00:32

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