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

Handle URI:
http://hdl.handle.net/10754/599052
Title:
On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
Authors:
Zygalakis, K. C.
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.
Citation:
Zygalakis KC (2011) On the Existence and the Applications of Modified Equations for Stochastic Differential Equations. SIAM Journal on Scientific Computing 33: 102–130. Available: http://dx.doi.org/10.1137/090762336.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2011
DOI:
10.1137/090762336
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorZygalakis, K. C.en
dc.date.accessioned2016-02-25T13:51:56Zen
dc.date.available2016-02-25T13:51:56Zen
dc.date.issued2011-01en
dc.identifier.citationZygalakis KC (2011) On the Existence and the Applications of Modified Equations for Stochastic Differential Equations. SIAM Journal on Scientific Computing 33: 102–130. Available: http://dx.doi.org/10.1137/090762336.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/090762336en
dc.identifier.urihttp://hdl.handle.net/10754/599052en
dc.description.abstractIn 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.en
dc.description.sponsorshipThis 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.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBackward error analysisen
dc.subjectHarmonic oscillatoren
dc.subjectLangevin equationen
dc.subjectMultiplicative noiseen
dc.subjectStochastic differential equationsen
dc.subjectWeak convergenceen
dc.titleOn the Existence and the Applications of Modified Equations for Stochastic Differential Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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