ON THE MULTILEVEL MONTE CARLO ESTIMATION OF UNBIASED EXPECTATION VIA SEQUENCE EXTRAPOLATION

摘要

This work develops variants of the multilevel Monte Carlo (MLMC) estimator for the estimation of unbiased statistical expectation. Standard MLMC estimators suffer from approximation error bias in the estimation of expectation. The new MLMC estimators are applicable to sequences of model approximations that have a rate-dependent decreasing approximation error that can be extrapolated to the zero error limit. Output quantities of interest of this form often arise in the numerical simulation of PDEs using a sequence of successively refined meshes. The new MLMC estimators exhibit a 2 x computational cost savings when compared to the biased MLMC estimator for this class of problems.