High-degree cubature on Wiener space through unshuffle expansions

Fuente: arXiv
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Main Authors: Ferrucci, Emilio, Herschell, Timothy, Litterer, Christian, Lyons, Terry
Format: Preprint
Published: 2024
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_version_ 1866914162282594304
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