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dc.contributor.authorHoel, Hakon
dc.contributor.authorHäppölä, Juho
dc.contributor.authorTempone, Raul
dc.date.accessioned2017-01-02T08:10:20Z
dc.date.available2017-01-02T08:10:20Z
dc.date.issued2016-06-14
dc.identifier.citationHoel H, Häppölä J, Tempone R (2016) Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods: 29–86. Available: http://dx.doi.org/10.1007/978-3-319-33507-0_2.
dc.identifier.issn2194-1009
dc.identifier.issn2194-1017
dc.identifier.doi10.1007/978-3-319-33507-0_2
dc.identifier.urihttp://hdl.handle.net/10754/622138
dc.description.abstractA formal mean square error expansion (MSE) is derived for Euler-Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise, a posteriori, adaptive time-stepping Euler-Maruyama algorithm for numerical solutions of SDE, and the resulting algorithm is incorporated into a multilevel Monte Carlo (MLMC) algorithm for weak approximations of SDE. This gives an efficient MSE adaptive MLMC algorithm for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC algorithm is shown to outperform the uniform time-stepping MLMC algorithm by orders of magnitude, producing output whose error with high probability is bounded by TOL > 0 at the near-optimal MLMC cost rate б(TOL log(TOL)) that is achieved when the cost of sample generation is б(1).
dc.publisherSpringer Nature
dc.subjectA posteriori error estimation
dc.subjectAdaptive methods
dc.subjectAdjoints
dc.subjectEuler-maruyama method
dc.subjectMultilevel monte carlo
dc.subjectStochastic differential equations
dc.titleConstruction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo
dc.typeConference Paper
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSpringer Proceedings in Mathematics & Statistics
dc.conference.date2014-04-06 to 2014-04-11
dc.conference.name11th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2014
dc.conference.locationLeuven, BEL
dc.contributor.institutionDepartment of Mathematics, University of Oslo, P.O. Box 1053, Blindern, Oslo, Norway
dc.identifier.arxivid1411.5515
kaust.personHoel, Hakon
kaust.personHäppölä, Juho
kaust.personTempone, Raul
dc.date.published-online2016-06-14
dc.date.published-print2016


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