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Multilevel Monte Carlo Methods

  • Stefan Heinrich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2179)

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.

Keywords

Banach Space Integral Equation Monte Carlo Method Multilevel Approach Multilevel Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Stefan Heinrich
    • 1
  1. 1.Fachbereich InformatikUniversität KaiserslauternGermany

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