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Free Groups and Signatures

In: Stochastic Analysis and Applications 2025

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  • Yves Le Jan

    (Université Paris-Saclay, Mathématique)

Abstract

The main purpose of this note is to propose a short review of the algebraic setting in which the notion of signature arises naturally, especially in connection with the lower central series of the free group, independently of the choice of a system of generators. Some formulas are given for the signature and the log-signature components. Finally, we show how the notion of signature can be extended to discrete paths on regular graphs.

Suggested Citation

  • Yves Le Jan, 2026. "Free Groups and Signatures," Springer Books, in: Dan Crisan & Ilya Chevyrev & Thomas Cass & James Foster & Christian Litterer & Cristopher Salvi (ed.), Stochastic Analysis and Applications 2025, pages 175-187, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-03914-9_6
    DOI: 10.1007/978-3-032-03914-9_6
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