MLMC techniques for discontinuous functions
Numerical Analysis
2023-09-06 v2 Numerical Analysis
Abstract
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower decay in the variance of the MLMC correction. This article reviews the literature on techniques which can be used to overcome this challenge in a variety of different contexts, and discusses recent developments using either a branching diffusion or adaptive sampling.
Cite
@article{arxiv.2301.02882,
title = {MLMC techniques for discontinuous functions},
author = {Michael B Giles},
journal= {arXiv preprint arXiv:2301.02882},
year = {2023}
}
Comments
15 pages, 6 figures, submitted to proceedings of MCQMC22 conference