High-degree cubature on Wiener space through unshuffle expansions

2024/11/20 by Ferrucci, Emilio, Herschell, Timothy, Litterer, Christian +1 · 2 citations
#60L90 #65C35 #65D32 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2411.13707

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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