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A multilevel approach towards unbiased sampling of random elliptic partial differential equations

Published online by Cambridge University Press:  29 November 2018

Xiaoou Li
Affiliation:
University of Minnesota
Jingchen Liu
Affiliation:
Columbia University
Shun Xu
Affiliation:
Columbia University
Corresponding
E-mail address:

Abstract

Partial differential equations are powerful tools for used to characterizing various physical systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper we present a Monte Carlo scheme that yields unbiased estimators for expectations of random elliptic partial differential equations. This algorithm combines a multilevel Monte Carlo method (Giles (2008)) and a randomization scheme proposed by Rhee and Glynn (2012), (2013). Furthermore, to obtain an estimator with both finite variance and finite expected computational cost, we employ higher-order approximations.

Type
Original Article
Copyright
Copyright © Applied Probability Trust 2018 

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References

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