High-degree cubature on Wiener space through unshuffle expansions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914162282594304 |
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| author | Ferrucci, Emilio Herschell, Timothy Litterer, Christian Lyons, Terry |
| author_facet | Ferrucci, Emilio Herschell, Timothy Litterer, Christian Lyons, Terry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-degree cubature on Wiener space through unshuffle expansions Ferrucci, Emilio Herschell, Timothy Litterer, Christian Lyons, Terry Probability 60L90, 65C35, 65D32 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. |
| title | High-degree cubature on Wiener space through unshuffle expansions |
| topic | Probability 60L90, 65C35, 65D32 |
| url | https://arxiv.org/abs/2411.13707 |