Mathematics > Probability
[Submitted on 20 Nov 2024]
Title:High-degree cubature on Wiener space through unshuffle expansions
View PDF HTML (experimental)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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