On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

K. C. Zygalakis

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)102-130
Number of pages29
JournalSIAM Journal on Scientific Computing
Volume33
Issue number1
DOIs
StatePublished - Jan 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was partially supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). It was also partially funded by a David Crighton Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Fingerprint

Dive into the research topics of 'On the Existence and the Applications of Modified Equations for Stochastic Differential Equations'. Together they form a unique fingerprint.

Cite this