Signatures of paths transformed by polynomial maps

DOI10.1007/s13366-020-00493-9zbMath1455.13051arXiv1812.05962OpenAlexW3014913828MaRDI QIDQ2204389

Rosa Preiß, Laura Colmenarejo

Publication date: 15 October 2020

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05962

zbMATH Keywords

iterated integralsshuffle producttensor algebrapolynomial mapshalf-shuffle algebrassignature tensors

Mathematics Subject Classification ID

Other nonassociative rings and algebras (17D99) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25) Signatures and data streams (60L10)

Related Items (6)

The moving-frame method for the iterated-integrals signature: orthogonal invariants ⋮ Generalized iterated-sums signatures ⋮ Nonlinear independent component analysis for discrete-time and continuous-time signals ⋮ Toric geometry of path signature varieties ⋮ New directions in rough path theory. Abstracts from the workshop held December 6--12, 2020 (online meeting) ⋮ A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula

Uses Software

• signature-invariants

Cites Work

• The signature of a rough path: uniqueness
• Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula
• Lie elements and an algebra associated with shuffles
• Uniqueness for the signature of a path of bounded variation and the reduced path group
• The rough Veronese variety
• Invariants of multidimensional time series based on their iterated-integral signature
• On the groups \(H(\Pi,n)\). I
• NATURAL ENDOMORPHISMS OF SHUFFLE ALGEBRAS
• Multidimensional Stochastic Processes as Rough Paths
• Noncommutative Geometry and Path Integrals
• Learning Paths from Signature Tensors
• VARIETIES OF SIGNATURE TENSORS
• CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
• A course on rough paths. With an introduction to regularity structures
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