• 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}
}
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… 
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Introduction to rough paths theory

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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