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

Xiaoou Li, Jingchen Liu, Shun Xu

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1007-1031
Number of pages25
JournalAdvances in Applied Probability
Volume50
Issue number4
DOIs
StatePublished - Dec 1 2018

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Elliptic Partial Differential Equations
Partial differential equations
Sampling
Multilevel Methods
Higher Order Approximation
Unbiased estimator
Probability Model
Randomisation
Measurement errors
Measurement Error
Monte Carlo method
Computational Cost
Monte Carlo methods
Partial differential equation
Estimator
Uncertainty
Costs

Keywords

  • 2010 Mathematics subject classification
  • Primary 65C05Secondary 35R6082B80

Cite this

A multilevel approach towards unbiased sampling of random elliptic partial differential equations. / Li, Xiaoou; Liu, Jingchen; Xu, Shun.

In: Advances in Applied Probability, Vol. 50, No. 4, 01.12.2018, p. 1007-1031.

Research output: Contribution to journalArticle

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