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H 1 An elementary proof of the reconstruction theorem

Auteurs : Teichmann, Josef (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Keywords : universal approximation, reconstruction theorem, regularity structures

    Codes MSC :

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 26/03/2021
      Date de captation : 09/03/2021
      Sous collection : Research talks
      arXiv category : Functional Analysis ; Probability
      Domaine : Mathematics in Science & Technology
      Durée : 00:46:45
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2021-03-09_Teichmann.mp4

    Informations sur la Rencontre Virtuelle

    Nom de la rencontre : Pathwise Stochastic Analysis and Applications / Analyse stochastique trajectorielle et applications
    Organisateurs de la rencontre : Coutin, Laure ; Gassiat, Paul ; Lejay, Antoine ; Marie, Nicolas ; Tindel, Samy
    Dates : 08/03/2021 - 12/03/2021
    Année de la rencontre : 2021
    URL Congrès : https://conferences.cirm-math.fr/2322.html

    Citation Data

    DOI : 10.24350/CIRM.V.19729003
    Cite this video as: Teichmann, Josef (2021). An elementary proof of the reconstruction theorem.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19729003
    URI : http://dx.doi.org/10.24350/CIRM.V.19729003

    Voir aussi


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