Publikation:

The geometry of controlled rough paths

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Datum

2025

Autor:innen

Riedel, Sebastian
Schmeding, Alexander
Tapia, Nikolas

Herausgeber:innen

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https://doi.org/10.1016/j.spa.2025.104594
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Angaben zur Forschungsförderung

Deutsche Forschungsgemeinschaft (DFG): FOR 2402
Deutsche Forschungsgemeinschaft (DFG): A06

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Open Access-Veröffentlichung

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Mathematik und Statistik: Publikationen
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Stochastic Processes and their Applications. Elsevier. 2025, 184, 104594. ISSN 0304-4149. Verfügbar unter: doi: 10.1016/j.spa.2025.104594

Zusammenfassung

We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dimensional) vector bundle and allows to define a opology on the total space, the collection of all controlled path spaces, which turns out to be Polish in the geometric case. The construction is intrinsic and based on a new approximation result for controlled rough paths. This framework turns well-known maps such as the rough integration map and the Itô–Lyons map into continuous (structure preserving) mappings. Moreover, it is compatible with previous constructions of interest in the stability theory for rough integration.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Continuous fields of Banach spaces, Rough paths, Controlled rough paths

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ISO 690GHANI VARZANEH, Mayzar, Sebastian RIEDEL, Alexander SCHMEDING, Nikolas TAPIA, 2025. The geometry of controlled rough paths. In: Stochastic Processes and their Applications. Elsevier. 2025, 184, 104594. ISSN 0304-4149. Verfügbar unter: doi: 10.1016/j.spa.2025.104594
BibTex
@article{GhaniVarzaneh2025-06geome-72788,
  title={The geometry of controlled rough paths},
  year={2025},
  doi={10.1016/j.spa.2025.104594},
  volume={184},
  issn={0304-4149},
  journal={Stochastic Processes and their Applications},
  author={Ghani Varzaneh, Mayzar and Riedel, Sebastian and Schmeding, Alexander and Tapia, Nikolas},
  note={Article Number: 104594}
}
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