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Convergence of numerical time-averaging and stationary measures via Poisson equations

dc.contributor.author Mattingly, JC
dc.contributor.author Stuart, AM
dc.contributor.author Tretyakov, MV
dc.date.accessioned 2011-06-21T17:27:53Z
dc.date.accessioned 2017-11-30T20:52:54Z
dc.date.available 2017-11-30T20:52:54Z
dc.date.issued 2010-07-07
dc.identifier.issn 0036-1429
dc.identifier.uri https://hdl.handle.net/10161/15777
dc.description.abstract Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
dc.language.iso en_US
dc.publisher Society for Industrial & Applied Mathematics (SIAM)
dc.relation.ispartof SIAM Journal on Numerical Analysis
dc.relation.isversionof 10.1137/090770527
dc.relation.replaces http://hdl.handle.net/10161/4314
dc.relation.replaces 10161/4314
dc.title Convergence of numerical time-averaging and stationary measures via Poisson equations
dc.title.alternative
dc.type Journal article
duke.contributor.id Mattingly, JC|0297691
dc.description.version Version of Record
duke.date.pubdate 2010-00-00
duke.description.issue 2
duke.description.volume 48
dc.relation.journal Siam Journal on Numerical Analysis
pubs.begin-page 552
pubs.end-page 577
pubs.issue 2
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Statistical Science
pubs.organisational-group Temp group - logins allowed
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 48
duke.contributor.orcid Mattingly, JC|0000-0002-1819-729X


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