High-degree cubature on Wiener space through unshuffle expansions

Emilio Ferrucci; Timothy Herschell; Christian Litterer; Terry Lyons

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arXiv · 2411.13707

High-degree cubature on Wiener space through unshuffle expansions

Emilio Ferrucci·Timothy Herschell·Christian Litterer·Terry Lyons

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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.

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Emilio Ferrucci, Timothy Herschell, Christian Litterer, Terry Lyons. 2024-11-20. High-degree cubature on Wiener space through unshuffle expansions. https://arxiv.org/abs/2411.13707

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