A Multilevel Approach towards Unbiased Sampling of Random Elliptic Partial Differential Equations
Probability
2016-05-23 v1
Abstract
Partial differential equation is a powerful tool to characterize various physics 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 multilevel Monte Carlo [Giles, 2008] and a randomization scheme proposed by [Rhee and Glynn, 2012, Rhee and Glynn, 2013]. Furthermore, to obtain an estimator with both finite variance and finite expected computational cost, we employ higher order approximations.
Cite
@article{arxiv.1605.06349,
title = {A Multilevel Approach towards Unbiased Sampling of Random Elliptic Partial Differential Equations},
author = {Xiaoou Li and Jingchen Liu},
journal= {arXiv preprint arXiv:1605.06349},
year = {2016}
}