Geodesic
Rough paths and SPDE
Ismael Bailleul1 ; Carlo Bellingeri2 ; Yvain Bruned3 ; Adeline Fermanian4 ; Nicolas Marie5
1Univ. Rennes, IRMAR - UMR CNRS 6625, 35000 Rennes, France
2TU Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany
3Univ. Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland
4Mines ParisTech - CBIO, Institut Curie, INSERM - U900, Sorbonne Université - LPSM, Paris, France
5Univ. Paris Nanterre, MODAL’X - UMR CNRS 9023, 92001 Nanterre, France
ESAIM. Proceedings, Tome 74 (2023), pp. 169-184
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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

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 
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     author = {Ismael Bailleul and Carlo Bellingeri and Yvain Bruned and Adeline Fermanian and Nicolas Marie},
     title = {Rough paths and {SPDE}},
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     pages = {169--184},
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     doi = {10.1051/proc/202374169},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202374169/}
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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

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