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Advances in Applied Probability Advances in Applied Probability

Article contents

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

Part of: Miscellaneous topics - Partial differential equations Equilibrium statistical mechanics Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  29 November 2018

Xiaoou Li ,
Jingchen Liu  and
Shun Xu
Xiaoou Li
Affiliation:
University of Minnesota
Jingchen Liu
Affiliation:
Columbia University
Shun Xu
Affiliation:
Columbia University
Corresponding
E-mail address:
xiaoou@stat.columbia.edu
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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.

Keywords

Unbiased sampling partial differential equations with random coefficients Monte Carlo method

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations 82B80: Numerical methods (Monte Carlo, series resummation, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 4 , December 2018 , pp. 1007 - 1031
Copyright
Copyright © Applied Probability Trust 2018 

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References

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