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arXiv · 2301.02882

MLMC techniques for discontinuous functions

Michael B Giles
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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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Michael B Giles. 2023-09-04. MLMC techniques for discontinuous functions. https://arxiv.org/abs/2301.02882

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