Multi-level Monte Carlo algorithms for infinite-dimensional integration on RN

  • Authors:

  • Fred J. Hickernell;Thomas Müller-Gronbach;Ben Niu;Klaus Ritter

  • Affiliations:

  • Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA;Fakultät für Informatik und Mathematik, Universität Passau, 94030 Passau, Germany;Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA;Fachbereich Mathematik, Technische Universität Darmstadt, Schloígartenstr.7, 64289 Darmstadt, Germany

  • Venue:
  • Journal of Complexity
  • Year:
  • 2010

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Abstract

We study randomized algorithms for numerical integration with respect to a product probability measure on the sequence space R^N. We consider integrands from reproducing kernel Hilbert spaces, whose kernels are superpositions of weighted tensor products. We combine tractability results for finite-dimensional integration with the multi-level technique to construct new algorithms for infinite-dimensional integration. These algorithms use variable subspace sampling, and we compare the power of variable and fixed subspace sampling by an analysis of minimal errors.