Smooth rough paths, their geometry and algebraic renormalization
- We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the key to a purely algebraic form of Lyons' extension theorem, the renormalization of rough paths following up on [Bruned et al.: A rough path perspective on renormalization, J. Funct. Anal. 277(11), 2019], as well as a related notion of "sum of rough paths". We first develop our ideas in a geometric rough path setting, as this best resonates with recent works on signature varieties, as well as with the renormalization of geometric rough paths. We then explore extensions to the quasi-geometric and the more general Hopf algebraic setting.
| Author details: | Carlo BellingeriORCiD, Peter FrizORCiDGND, Sylvie PaychaORCiDGND, Rosa Lili Dora PreißORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s10013-022-00570-7 |
| ISSN: | 2305-221X |
| ISSN: | 2305-2228 |
| Title of parent work (English): | Vietnam journal of mathematics |
| Publisher: | Springer |
| Place of publishing: | Singapore |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/06/23 |
| Publication year: | 2022 |
| Release date: | 2024/01/31 |
| Tag: | Cartan's development; Renormalization; Rough paths; Signatures |
| Volume: | 50 |
| Issue: | 3 |
| Number of pages: | 43 |
| First page: | 719 |
| Last Page: | 761 |
| Funding institution: | DFG Research Unit [FOR2402]; European Research Council (ERC) under the; European Union [683164] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Hybrid Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
