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H 2 Nonconventional limit theorems in probability and dynamical systems

Auteurs : Kifer, Yuri (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We discuss various limit theorems for "nonconventional" sums of the form $\sum ^N_{n=1}F\left ( \xi \left ( n \right ),\xi \left ( 2n \right ),...,\xi \left ( \ell n \right ) \right )$ where $\xi \left ( n \right )$ is a stochastic process or a dynamical system. The motivation for this study comes, in particular, from many papers about nonconventional ergodic theorems appeared in the last 30 years. Such limit theorems describe multiple recurrence properties of corresponding stochastic processes and dynamical systems. Among our results are: central limit theorem, a.s. central limit theorem, local limit theorem, large deviations and averaging. Some multifractal type questions and open problems will be discussed, as well.
    Keywords : limit theorems - nonconventional sums - multiple recurrence

    Codes MSC :
    37A50 - Relations with probability theory and stochastic processes
    37D35 - Thermodynamic formalism, variational principles, equilibrium states
    60F05 - Central limit and other weak theorems

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 22/08/14
      Date de captation : 07/07/14
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Probability and Statistics
      Format : quicktime ; audio/x-aac
      Durée : 00:54:22
      Domaine : Dynamical Systems & ODE ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-07-07_Kifer.mp4

    Informations sur la rencontre

    Nom de la rencontre : Limit theorems in dynamics and applications / Théorèmes limites en dynamique et applications
    Organisateurs de la rencontre : Olla, Stefano ; Reinert, Gesine ; Vaienti, Sandro ; Volny, Dalibor
    Dates : 07/07/14 - 11/07/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18578303
    Cite this video as: Kifer, Yuri (2014). Nonconventional limit theorems in probability and dynamical systems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18578303
    URI : http://dx.doi.org/10.24350/CIRM.V.18578303


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