Rough paths and SPDE

Ismael Bailleul; Carlo Bellingeri; Yvain Bruned; Adeline Fermanian; Nicolas Marie

doi:10.1051/proc/202374169

Geodesic

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Rough paths and SPDE

Ismael Bailleul ¹ ; Carlo Bellingeri ² ; Yvain Bruned ³ ; Adeline Fermanian ⁴ ; Nicolas Marie ⁵

¹ Univ. Rennes, IRMAR - UMR CNRS 6625, 35000 Rennes, France
² TU Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany
³ Univ. Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland
⁴ Mines ParisTech - CBIO, Institut Curie, INSERM - U900, Sorbonne Université - LPSM, Paris, France
⁵ Univ. Paris Nanterre, MODAL’X - UMR CNRS 9023, 92001 Nanterre, France

ESAIM. Proceedings, Tome 74 (2023), pp. 169-184.

Voir la notice de l'article provenant de la source EDP Sciences

Résumé

After a brief survey on rough paths theory, from the seminal paper of T. Lyons to its recent developments, this proceeding provides details on C. Bellingeri, Y. Bruned and A. Fermanian’s talks during the Journées MAS 2020: a new formulation and a generalization of the signature operator, an extension of branched rough paths called Volterra branched rough paths, and recurrent neural networks investigated as a kernel method thanks to the signature operator and neural ODEs.

DOI : 10.1051/proc/202374169

Affiliations des auteurs :

Ismael Bailleul ¹ ; Carlo Bellingeri ² ; Yvain Bruned ³ ; Adeline Fermanian ⁴ ; Nicolas Marie ⁵

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Ismael Bailleul; Carlo Bellingeri; Yvain Bruned; Adeline Fermanian; Nicolas Marie. Rough paths and SPDE. ESAIM. Proceedings, Tome 74 (2023), pp. 169-184. doi : 10.1051/proc/202374169. http://geodesic.mathdoc.fr/articles/10.1051/proc/202374169/

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