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

Xiaoou Li, Jingchen Liu, Shun Xu

Research output: Contribution to journalArticle

1 Scopus citations


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
Issue number4
StatePublished - Dec 1 2018



  • 2010 Mathematics subject classification
  • Primary 65C05Secondary 35R6082B80

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