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An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorMancini, Sara
dc.contributor.authorBernal Martínez, Francisco Manuel
dc.contributor.authorAcebrón, Juan Antonio
dc.date.accessioned2021-03-11T09:59:06Z
dc.date.available2021-03-11T09:59:06Z
dc.date.issued2016-02
dc.description.abstractThe numerical approximation of boundary value problems by means of a probabilistic representations often has the drawback that the Monte Carlo estimate of the solution is substantially biased due to the presence of the domain boundary. We introduce a scheme, which we have called the leading-term Monte Carlo regression, which seeks to remove that bias by replacing a ’cloud’ of Monte Carlo estimates—carried out at different discretization levels—for the usual single Monte Carlo estimate. The practical result of our scheme is an acceleration of the Monte Carlo method. Theoretical analysis of the proposed scheme, confirmed by numerical experiments, shows that the achieved speedup can be well over 100.en
dc.description.sponsorshipThis work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) under grants UID/CEC/50021/2013, and PTDC/EIA-CCO/098910/2008. FB also acknowledges FCT funding under grant SFRH/BPD/79986/2011.en
dc.format.extent21
dc.identifier.bibliographicCitationMancini, S., Bernal, F., Acebrón, J. A. (2016). An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems. Journal of Scientific Computing, 66(2), 577–597.en
dc.identifier.doihttps://doi.org/10.1007/s10915-015-0033-4
dc.identifier.issn0885-7474
dc.identifier.publicationfirstpage577
dc.identifier.publicationissue2
dc.identifier.publicationlastpage597
dc.identifier.publicationtitleJournal of Scientific Computingen
dc.identifier.publicationvolume66
dc.identifier.urihttps://hdl.handle.net/10016/32112
dc.identifier.uxxiAR/0000026518
dc.language.isoeng
dc.publisherSpringer Natureen
dc.rightsCopyright © 2015, Springer Science Business Media New Yorken
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.subject.otherMonte Carlo methoden
dc.subject.otherRomberg extrapolationen
dc.subject.otherBounded difusiónen
dc.subject.otherFeynman-Kac formulaen
dc.subject.otherFirst exit timeen
dc.subject.otherParallel computingen
dc.titleAn Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problemsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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