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Estimation of arbitrary order central statistical moments by the multilevel Monte Carlo method

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Abstract

We extend the general framework of the Multilevel Monte Carlo method to multilevel estimation of arbitrary order central statistical moments. In particular, we prove that under certain assumptions, the total cost of an MLMC central moment estimator is asymptotically the same as the cost of the multilevel sample mean estimator and thereby is asymptotically the same as the cost of a single deterministic forward solve. The general convergence theory is applied to a class of obstacle problems with rough random obstacle profiles. Numerical experiments confirm theoretical findings.

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Acknowledgments

The major part of the research presented in this paper has been carried out at the Department of Mathematics and Statistics, University of Reading, United Kingdom. The authors acknowledge support by the University of Reading and the University of Oldenburg.

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Authors and Affiliations

  1. Institute for Mathematics, Carl von Ossietzky University, 26111, Oldenburg, Germany

    Claudio Bierig & Alexey Chernov

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  1. Claudio Bierig
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  2. Alexey Chernov
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Correspondence to Alexey Chernov.

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Bierig, C., Chernov, A. Estimation of arbitrary order central statistical moments by the multilevel Monte Carlo method. Stoch PDE: Anal Comp 4, 3–40 (2016). https://doi.org/10.1007/s40072-015-0063-9

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  • DOI: https://doi.org/10.1007/s40072-015-0063-9

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