Multilevel Monte Carlo Methods

Authors:
Stefan Heinrich
Affiliations:
-
Venue:
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Year:
2001

Citing 6
Cited 7

Information-based complexity

Information-based complexity
Discrete-stochastic procedures for the global estimation of an integral which depends on a parameter

Computational Mathematics and Mathematical Physics
Monte Carlo complexity of global solution of integral equations

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Hierarchical Monte Carlo image synthesis

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Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems

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Journal of Complexity
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Winter Simulation Conference
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Computing mean first exit times for stochastic processes using multi-level Monte Carlo

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Multilevel Monte Carlo methods for highly heterogeneous media

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A multi-level Monte Carlo FPGA accelerator for option pricing in the Heston model

Proceedings of the Conference on Design, Automation and Test in Europe
Multilevel Monte Carlo for two phase flow and Buckley-Leverett transport in random heterogeneous porous media

Journal of Computational Physics

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Abstract

We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the 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.