| Issue |
ESAIM: M2AN
Volume 58, Number 6, November-December 2024
Special issue - To commemorate Assyr Abdulle
|
|
|---|---|---|
| Page(s) | 2287 - 2316 | |
| DOI | https://doi.org/10.1051/m2an/2024039 | |
| Published online | 04 December 2024 | |
Complexity analysis of quasi continuous level Monte Carlo*
Institute of Applied Analysis and Numerical Simulation (IANS), University of Stuttgart, Allmandring 5b, 70569 Stuttgart, Germany
** Corresponding author: cedric.beschle@ians.uni-stuttgart.de
Received:
25
May
2023
Accepted:
20
May
2024
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest. Continuous level Monte Carlo methods allow naturally for samplewise adaptive mesh refinements, which are indicated by (goal-oriented) error estimators. The samplewise refinement levels are drawn in the estimator from an exponentially-distributed random variable. Unfortunately in practical examples this results in higher costs due to high variance in the samples. In this paper we propose a variant of continuous level Monte Carlo, where a quasi Monte Carlo sequence is utilized to “sample” the exponential random variable. We provide a complexity theorem for this novel estimator and show that this theoretically and practically results in a variance reduction of the whole estimator.
Mathematics Subject Classification: 65C05 / 65C10 / 11K38 / 65N30 / 65N50
Key words: Uncertainty quantification / Monte Carlo methods / continuous level Monte Carlo
© The authors. Published by EDP Sciences, SMAI 2024
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