Internet publication
High-degree cubature on Wiener space through unshuffle expansions
- Abstract:
- Utilising classical results on the structure of Hopf algebras, we develop a novel approach for the construction of cubature formulae on Wiener space based on unshuffle expansions. We demonstrate the effectiveness of this approach by constructing the first explicit degree-7 cubature formula on d-dimensional Wiener space with drift, in the sense of Lyons and Victoir. The support of our degree-7 formula is significantly smaller than that of currently implemented or proposed constructions.
- Publication status:
- Published
- Peer review status:
- Not peer reviewed
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- Files:
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(Preview, Version of record, pdf, 294.8KB, Terms of use)
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- Publisher copy:
- 10.48550/arXiv.2411.13707
Authors
- Host title:
- arXiv
- Publication date:
- 2024-11-20
- DOI:
- EISSN:
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2331-8422
- Language:
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English
- Pubs id:
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2064468
- Local pid:
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pubs:2064468
- Deposit date:
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2025-01-08
Terms of use
- Copyright holder:
- Ferrucci et al
- Copyright date:
- 2024
- Rights statement:
- ©2024 The Authors. This paper is an open access article distributed under the terms of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)
- Licence:
- CC Attribution (CC BY)
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