H 2 Statistical inverse problems and geometric "wavelet" construction

Auteurs : Kerkyacharian, Gérard (Auteur de la Conférence)
CIRM (Editeur )

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inverse problem : toy model wavelet frame on R construction of needlet regularity of gaussian process in geometrical framework

Résumé : In the fist part of the talk, we will look to some statistical inverse problems for which the natural framework is no more an Euclidian one.
In the second part we will try to give the initial construction of (not orthogonal) wavelets -of the 80 - by Frazier, Jawerth,Weiss, before the Yves Meyer ORTHOGONAL wavelets theory.
In the third part we will propose a construction of a geometric wavelet theory. In the Euclidian case, Fourier transform plays a fundamental role. In the geometric situation this role is given to some "Laplacian operator" with some properties.
In the last part we will show that the previous theory could help to revisit the topic of regularity of Gaussian processes, and to give a criterium only based on the regularity of the covariance operator.

Codes MSC :
42C15 - General harmonic expansions, frames
43A80 - Analysis on other specific Lie groups, See also {22Exx}
43A85 - Analysis on homogeneous spaces
46E35 - Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
58J35 - Heat and other parabolic equation methods
62G05 - Nonparametric estimation
62G08 62G10 - Nonparametric hypothesis testing
62G20 - Nonparametric asymptotic efficiency

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 02/03/2016
    Date de captation : 10/02/2016
    Collection : Probability and Statistics
    Sous collection : Research talks
    Domaine : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 02:23:57
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-02-10-11_kerkyacharian.mp4

Informations sur la rencontre

Nom de la rencontre : Thematic month on statistics - Week 2 : Mathematical statistics and inverse problems / Mois thématique sur les statistiques - Semaine 2 : statistiques mathématiques et problèmes inverses
Organisateurs de la rencontre : Autin, Florent ; Golubev, Yuri ; Pouet, Christophe
Dates : 08/02/2016 - 12/02/2016
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1616.html

Citation Data

DOI : 10.24350/CIRM.V.18926703
Cite this video as: Kerkyacharian, Gérard (2016). Statistical inverse problems and geometric "wavelet" construction. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18926703
URI : http://dx.doi.org/10.24350/CIRM.V.18926703

Voir aussi


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  • T. Coulhon, G. Kerkyacharian, P. Petrushev, Heat kernel generated frames in the setting of Dirichlet spaces, J. Fourier Anal. Appl. 18 (2012), 995-1066. - dx.doi.org/10.1007/s00041-012-9232-7

  • M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley theory and the study of function spaces, CBMS No 79 (1991), AMS. - http://bookstore.ams.org/cbms-79

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