Towards automatic global error control: Computable weak error expansion for the tau-leap method

Handle URI:
http://hdl.handle.net/10754/561695
Title:
Towards automatic global error control: Computable weak error expansion for the tau-leap method
Authors:
Karlsson, Peer Jesper; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms, a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie Algorithm or the Stochastic Simulation Slgorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term. © de Gruyter 2011.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Stochastic Numerics Research Group
Publisher:
De Gruyter
Journal:
Monte Carlo Methods and Applications
Issue Date:
Jan-2011
DOI:
10.1515/MCMA.2011.011
ARXIV:
arXiv:1004.2948
Type:
Article
ISSN:
09299629
Additional Links:
http://arxiv.org/abs/arXiv:1004.2948v3
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKarlsson, Peer Jesperen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-08-03T09:02:29Zen
dc.date.available2015-08-03T09:02:29Zen
dc.date.issued2011-01en
dc.identifier.issn09299629en
dc.identifier.doi10.1515/MCMA.2011.011en
dc.identifier.urihttp://hdl.handle.net/10754/561695en
dc.description.abstractThis work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms, a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie Algorithm or the Stochastic Simulation Slgorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term. © de Gruyter 2011.en
dc.publisherDe Gruyteren
dc.relation.urlhttp://arxiv.org/abs/arXiv:1004.2948v3en
dc.subjectA posteriori error estimatesen
dc.subjectBackward dual functionsen
dc.subjectError estimationen
dc.subjectMarkov chainen
dc.subjectReaction networksen
dc.subjectTau-leapen
dc.subjectWeak approximationen
dc.titleTowards automatic global error control: Computable weak error expansion for the tau-leap methoden
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalMonte Carlo Methods and Applicationsen
dc.identifier.arxividarXiv:1004.2948en
kaust.authorKarlsson, Peer Jesperen
kaust.authorTempone, Raulen
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