The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures

Abstract

We establish well-definedness of the barycenter for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). Our main motivation stems from measures induced by iterated-integrals signatures.Comment: 49 pages, 1 figur