MLMC techniques for discontinuous functions

2023/01/07 by Michael B. Giles, Giles, Michael B · 1 citation
Computer Science · Materials Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Electron and X-Ray Spectroscopy Techniques #FOS: Mathematics #NMR spectroscopy and applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2301.02882

openalex publication_date 2023/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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