• Corpus ID: 247411237

# The geometry of controlled rough paths

@inproceedings{Varzaneh2022TheGO,
title={The geometry of controlled rough paths},
author={Mazyar Ghani Varzaneh and Sebastian Riedel and Alexander Schmeding and Nikolas Tapia},
year={2022}
}
• Published 11 March 2022
• Mathematics
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 topology 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…
1 Citations
• Computer Science
• 2023
These notes are an extended version of the course Introduction to rough paths theory'' given at the XXV Brazilian School of Probability in Campinas in August 2022. Their aim is to give a consise

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