00:00:00 / 00:00:00

Appears in collection : Pathwise Stochastic Analysis and Applications / Analyse stochastique trajectorielle et applications

The reconstruction theorem, a cornerstone of Martin Hairer’s theory of regularity structures,appears in this article as the unique extension of the explicitly given reconstruction operatoron the set of smooth models due its inherent Lipschitz properties. This new proof is a directconsequence of constructions of mollification procedures on spaces of models and modelled distributions: more precisely, for an abstract model Z of a given regularity structure, a mollifiedmodel is constructed, and additionally, any modelled distribution f can be approximated byelements of a universal subspace of modelled distribution spaces. These considerations yield inparticular a non-standard approximation results for rough path theory. All results are formulatedin a generic (p, q) Besov setting. There are also implications on learning solution maps from amachine learning perspective.Joint work with Harprit Singh.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19729003
  • Cite this video Teichmann, Josef (09/03/2021). An elementary proof of the reconstruction theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19729003
  • URL https://dx.doi.org/10.24350/CIRM.V.19729003

Bibliography

  • SINGH, Harprit et TEICHMANN, Josef. An elementary proof of the reconstruction theorem. arXiv preprint arXiv:1812.03082, 2018. - https://arxiv.org/abs/1812.03082

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback