Decomposing tensor spaces via path signatures

The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. We show that the parametrization of this variety in...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2025-01, Vol.229 (1), p.107807, Article 107807
Main Authors: Améndola, Carlos, Galuppi, Francesco, Ríos Ortiz, Ángel David, Santarsiero, Pierpaola, Seynnaeve, Tim
Format: Article
Language:English
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Summary:The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature variety. We show that the parametrization of this variety induces a natural decomposition of the tensor space via representation theory, and connect this to the study of path invariants. We also reveal certain constraints that apply to the rank and symmetry of a signature tensor.
ISSN:0022-4049
DOI:10.1016/j.jpaa.2024.107807