A multilevel approach towards unbiased sampling of random elliptic partial differential equations. (29th November 2018)

• Record Type: Journal Article
• Authors: Li, Xiaoou; Liu, Jingchen; Xu, Shun
• Is Part Of: Advances in applied probability. Volume 50:Number 4(2018)
• Page Start: 1007
• Page End: 1031
• Publication Date: 2018-11-29
• Subjects: Unbiased sampling, -- partial differential equations with random coefficients, -- Monte Carlo method; Primary 65C05, -- Secondary 35R60, -- 82B80; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2018.49
• Languages: English
• ISSNs: 0001-8678

Abstract

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.