Report
Smooth rough paths, their geometry and algebraic renormalization
| Title: | Smooth rough paths, their geometry and algebraic renormalization |
|---|---|
| Authors: | Carlo, Bellingeri, Peter K., Friz, Sylvie, Paycha, Rosa, Preiß |
| Publication Year: | 2021 |
| Collection: | Weierstrass Institute for Applied Analysis and Stochastics publication server |
| Subject Terms: | article, ddc:510 |
| Description: | 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 in the spirit of [Bruned, Chevyrev, Friz, Preiß, 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 the renormalization of geometric rough paths. We then explore extensions to the quasi-geometric and the more general Hopf algebraic setting. |
| Document Type: | report |
| Language: | English |
| Relation: | https://doi.org/10.48550/arXiv.2111.15539; https://archive.wias-berlin.de/receive/wias_mods_00007158; https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00003558/2111.15539.pdf; https://arxiv.org/abs/2111.15539 |
| DOI: | 10.48550/arXiv.2111.15539 |
| Availability: | https://doi.org/10.48550/arXiv.2111.15539 https://archive.wias-berlin.de/receive/wias_mods_00007158 https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00003558/2111.15539.pdf https://arxiv.org/abs/2111.15539 |
| Rights: | all rights reserved ; info:eu-repo/semantics/openAccess |
| Accession Number: | edsbas.F88DD5F5 |
| Database: | BASE |
| Description not available. |