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Fractional signature: A generalisation of the signature inspired by fractional calculus

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  • Corcuera, José Manuel
  • Jiménez, Rubén

Abstract

In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the signature, inspired by the previous one, but more convenient to use in machine learning. Finally, we test this last signature in a toy application to the problem of handwritten digit recognition, where significant improvements in accuracy rates are observed compared to those of the original signature.

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  • Corcuera, José Manuel & Jiménez, Rubén, 2026. "Fractional signature: A generalisation of the signature inspired by fractional calculus," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001786
    DOI: 10.1016/j.spl.2025.110533
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