MLMC techniques for discontinuous functions
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 revie...
| Main Author: | |
|---|---|
| Format: | Conference item |
| Language: | English |
| Published: |
Springer
2024
|
| _version_ | 1811140644010196992 |
|---|---|
| author | Giles, MB |
| author_facet | Giles, MB |
| author_sort | Giles, MB |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:32:52Z |
| format | Conference item |
| id | oxford-uuid:13a94aa3-ce3e-4ee5-83cb-13ce2166c50c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:25:15Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:13a94aa3-ce3e-4ee5-83cb-13ce2166c50c2024-08-23T12:04:13ZMLMC techniques for discontinuous functionsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:13a94aa3-ce3e-4ee5-83cb-13ce2166c50cEnglishSymplectic ElementsSpringer2024Giles, MBThe 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. |
| spellingShingle | Giles, MB MLMC techniques for discontinuous functions |
| title | MLMC techniques for discontinuous functions |
| title_full | MLMC techniques for discontinuous functions |
| title_fullStr | MLMC techniques for discontinuous functions |
| title_full_unstemmed | MLMC techniques for discontinuous functions |
| title_short | MLMC techniques for discontinuous functions |
| title_sort | mlmc techniques for discontinuous functions |
| work_keys_str_mv | AT gilesmb mlmctechniquesfordiscontinuousfunctions |