Multilevel hybrid Chernoff tau-leap

Handle URI:
http://hdl.handle.net/10754/557225
Title:
Multilevel hybrid Chernoff tau-leap
Authors:
Moraes, Alvaro ( 0000-0003-4144-1243 ) ; Tempone, Raul ( 0000-0003-1967-4446 ) ; Vilanova, Pedro ( 0000-0001-6620-6261 )
Abstract:
In this work, we extend the hybrid Chernoff tau-leap method to the multilevel Monte Carlo (MLMC) setting. Inspired by the work of Anderson and Higham on the tau-leap MLMC method with uniform time steps, we develop a novel algorithm that is able to couple two hybrid Chernoff tau-leap paths at different levels. Using dual-weighted residual expansion techniques, we also develop a new way to estimate the variance of the difference of two consecutive levels and the bias. This is crucial because the computational work required to stabilize the coefficient of variation of the sample estimators of both quantities is often unaffordable for the deepest levels of the MLMC hierarchy. Our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This is achieved with nearly optimal computational work. Indeed, the computational complexity of our method is of order O(TOL−2), the same as with an exact method, but with a smaller constant. Our numerical examples show substantial gains with respect to the previous single-level approach and the Stochastic Simulation Algorithm.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Multilevel hybrid Chernoff tau-leap 2015 BIT Numerical Mathematics
Journal:
BIT Numerical Mathematics
Issue Date:
8-Apr-2015
DOI:
10.1007/s10543-015-0556-y
ARXIV:
arXiv:1403.2943
Type:
Article
ISSN:
0006-3835; 1572-9125
Additional Links:
http://link.springer.com/10.1007/s10543-015-0556-y; http://arxiv.org/abs/1403.2943
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMoraes, Alvaroen
dc.contributor.authorTempone, Raulen
dc.contributor.authorVilanova, Pedroen
dc.date.accessioned2015-06-18T07:23:15Zen
dc.date.available2015-06-18T07:23:15Zen
dc.date.issued2015-04-08en
dc.identifier.citationMultilevel hybrid Chernoff tau-leap 2015 BIT Numerical Mathematicsen
dc.identifier.issn0006-3835en
dc.identifier.issn1572-9125en
dc.identifier.doi10.1007/s10543-015-0556-yen
dc.identifier.urihttp://hdl.handle.net/10754/557225en
dc.description.abstractIn this work, we extend the hybrid Chernoff tau-leap method to the multilevel Monte Carlo (MLMC) setting. Inspired by the work of Anderson and Higham on the tau-leap MLMC method with uniform time steps, we develop a novel algorithm that is able to couple two hybrid Chernoff tau-leap paths at different levels. Using dual-weighted residual expansion techniques, we also develop a new way to estimate the variance of the difference of two consecutive levels and the bias. This is crucial because the computational work required to stabilize the coefficient of variation of the sample estimators of both quantities is often unaffordable for the deepest levels of the MLMC hierarchy. Our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This is achieved with nearly optimal computational work. Indeed, the computational complexity of our method is of order O(TOL−2), the same as with an exact method, but with a smaller constant. Our numerical examples show substantial gains with respect to the previous single-level approach and the Stochastic Simulation Algorithm.en
dc.relation.urlhttp://link.springer.com/10.1007/s10543-015-0556-yen
dc.relation.urlhttp://arxiv.org/abs/1403.2943en
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s10543-015-0556-yen
dc.titleMultilevel hybrid Chernoff tau-leapen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalBIT Numerical Mathematicsen
dc.eprint.versionPost-printen
dc.identifier.arxividarXiv:1403.2943en
kaust.authorMoraes, Alvaroen
kaust.authorTempone, Raulen
kaust.authorVilanova, Pedroen
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