Journal article

Analysis of nested multilevel Monte Carlo using approximate Normal random variables

Abstract:: The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables which can be computed much more cheaply. A nested MLMC approach is adopted in which a twolevel treatment of the approximated random variables is embedded within a standard MLMC application. We analyse the resulting nested MLMC variance in the specific context of an SDE discretisation in which Normal random variables can be replaced by approximately Normal random variables, and provide numerical results to support the analysis.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Giles, M., & Sheridan-Methven, O. (2022). Analysis of nested multilevel Monte Carlo using approximate Normal random variables. SIAM/ASA Journal on Uncertainty Quantification, 10(1), 200–226.

MLA Style

Giles, M., and O. Sheridan-Methven. “Analysis of Nested Multilevel Monte Carlo Using Approximate Normal Random Variables.” SIAM/ASA Journal on Uncertainty Quantification, vol. 10, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 200–26.

Chicago Style

Giles, M, and O Sheridan-Methven. 2022. “Analysis of Nested Multilevel Monte Carlo Using Approximate Normal Random Variables.” SIAM/ASA Journal on Uncertainty Quantification 10 (1): 200–226.
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Files:: Giles_Sheridan_Methven_2021_Analysis_of_nested.pdf

(Preview, Accepted manuscript, 584.9KB, Terms of use)

Publisher copy:: 10.1137/21M1399385

Authors

+ Giles, M More by this author

Institution:: University of Oxford
Department:: MATHEMATICAL INSTITUTE
Sub department:: Mathematical Institute
Oxford college:: St Hugh's College
Role:: Author
ORCID:: 0000-0002-5445-3721

+ Sheridan-Methven, O More by this author

Role:: Author

+ Engineering and Physical Sciences Research Council More from this funder

Funder identifier:: http://dx.doi.org/10.13039/501100000266
Grant:: EP/P020720/1; EP/H05183X/1; MA/3630057; EP/E031455/1

Publisher:: Society for Industrial and Applied Mathematics
Journal:: SIAM/ASA Journal on Uncertainty Quantification More from this journal
Volume:: 10
Issue:: 1
Pages:: 200-226
Publication date:: 2022-02-08
Acceptance date:: 2021-09-27
DOI:: 10.1137/21M1399385
EISSN:: 2166-2525

Language:: English
Keywords:: FFR
Pubs id:: 1197041
Local pid:: pubs:1197041
Deposit date:: 2021-09-30

Terms of use

Copyright holder:: Society for Industrial and Applied Mathematics and American Statistical Association
Copyright date:: 2022
Rights statement:: © 2022 Society for Industrial and Applied Mathematics and American Statistical Association
Notes:: This is the accepted manuscript version of the article. The final version is available online from Society for Industrial and Applied Mathematics at: https://doi.org/10.1137/21M1399385

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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