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An elementary proof of the reconstruction theorem

De Josef Teichmann

universal approximation, reconstruction theorem, regularity structures

Apparaît dans la 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.

Informations sur la vidéo

Date de captation 09/03/2021
Date de publication 26/03/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19729003
Citer cette vidéo 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

Domaine(s)

Bibliographie

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

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