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H 1 Fast slow systems with chaotic noise

Auteurs : Kelly, David (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the statistical properties of chaotic systems can be well approximated by stochastic differential equations. In this talk, we focus on fast-slow ODEs, where the fast, chaotic variables are fed into the slow variables to yield a diffusion approximation. In particular we focus on the case where the chaotic noise is multidimensional and multiplicative. The tools from rough path theory prove useful in this difficult setting.

    Codes MSC :
    37A50 - Relations with probability theory and stochastic processes
    37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
    37D25 - Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
    60H10 - Stochastic ordinary differential equations

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 27/05/15
      Date de captation : 12/05/15
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Probability and Statistics
      Format : quicktime ; audio/x-aac
      Durée : 00:56:46
      Domaine : Dynamical Systems & ODE ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-05-12_Kelly.mp4

    Informations sur la rencontre

    Nom de la rencontre : Averaging and homogenization in deterministic and stochastic systems / Moyennisation et homogénéisation dans les systèmes déterministes et stochastiques
    Organisateurs de la rencontre : Liverani, Carlangelo ; Melbourne, Ian ; Pavliotis, Grigorios ; Olla, Stefano
    Dates : 11/05/15 - 15/05/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1198.html

    Citation Data

    DOI : 10.24350/CIRM.V.18763403
    Cite this video as: Kelly, David (2015). Fast slow systems with chaotic noise. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18763403
    URI : http://dx.doi.org/10.24350/CIRM.V.18763403


    Bibliographie

    1. Kelly, D., & Melbourne, I. (2014). Deterministic homogenization for fast-slow systems with chaotic noise. - http://arxiv.org/abs/1409.5748

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