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Multilevel Monte Carlo Methods

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Large-Scale Scientific Computing (LSSC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2179))

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Abstract

We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced bythe author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are given for the case where an approximation of the full solution function or a family of functionals of the solution depending on a parameter of a certain dimension is sought.

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, D-67653, Kaiserslautern, Germany

    Stefan Heinrich

Authors
  1. Stefan Heinrich
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad G. Bontchev, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. DTU, UNI•C, Danish IT Centre for Education and Research, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

  3. University of Rousse, Studentska 8, 7017, Rousse, Bulgaria

    Plamen Yalamov

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© 2001 Springer-Verlag Berlin Heidelberg

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Heinrich, S. (2001). Multilevel Monte Carlo Methods. In: Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2001. Lecture Notes in Computer Science, vol 2179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45346-6_5

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  • DOI: https://doi.org/10.1007/3-540-45346-6_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43043-8

  • Online ISBN: 978-3-540-45346-8

  • eBook Packages: Springer Book Archive

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