The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures
| Autor: | Clausel, Marianne, Diehl, Joscha, Mignot, Raphael, Schmitz, Leonard, Sugiura, Nozomi, Usevich, Konstantin |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). We provide two algorithms for computing it, using methods from Lie theory (namely, the Baker-Campbell-Hausdorff formula) and from the theory of Gr\"obner bases of modules. Our main motivation stems from measures induced by iterated-integrals signatures, and we calculate the barycenter for the signature of the Brownian motion. Comment: 48 pages, 1 figure |
| Databáze: | arXiv |
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