Estimation of arbitrary order central statistical moments by the multilevel Monte Carlo method

Abstract

We extend the general framework of the Multilevel Monte Carlo method to multilevel estimation of arbitrary order central statistical moments. In particular, we prove that under certain assumptions, the total cost of an MLMC central moment estimator is asymptotically the same as the cost of the multilevel sample mean estimator and thereby is asymptotically the same as the cost of a single deterministic forward solve. The general convergence theory is applied to a class of obstacle problems with rough random obstacle profiles. Numerical experiments confirm theoretical findings.