Central limit theorems for multilevel Monte Carlo methods
Artikel i vetenskaplig tidskrift, 2019

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT is achieved. In particular, if the variance decay rate dominates the computational cost rate (i.e., β>γ), we prove that the CLT applies to the standard (variance minimizing) MLMC estimator. For other settings where the CLT may not apply to the standard MLMC estimator, we propose an alternative estimator, called the mass-shifted MLMC estimator, to which the CLT always applies. This comes at a small efficiency loss: the computational cost of achieving mean square approximation error O(ϵ 2 ) is at worst a factor O(log(1∕ϵ)) higher with the mass-shifted estimator than with the standard one.

Central limit theorem

Multilevel Monte Carlo

Författare

Håkon Hoel

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Sebastian Krumscheid

Ecole Polytechnique Federale De Lausanne

Journal of Complexity

0885-064X (ISSN) 1090-2708 (eISSN)

Vol. 54 101407

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

Reglerteknik

Signalbehandling

DOI

10.1016/j.jco.2019.05.001

Mer information

Senast uppdaterat

2019-08-26