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Trois chemins contrôlés

Editor

Listed:
  • Gubinelli, Massimiliano

Author

Listed:
  • Chouk, Khalil

Abstract

In this thesis we propose to give some applications and generalizations of the theory of controlled rough paths, which can be summarized under three headings :- Getting a "good" notions of rough sheet which allows the construction of two dimensional integral driven by an irregular noise andobtain a change of variable formula for the fractional Brownian sheet or more generally a Gaussian sheet.- Construction of local and global solution for a large class of dispersive equations with an irregular modulation in the dispersion term using the nonlinear Young integral and the notion of controlled path.- Rigourous Interpretation of the stochastic quantization equation in the 3 dimensional torus and the construction of a local solution for this equation using the notion of controlled distribution.

Suggested Citation

  • Chouk, Khalil, 2014. "Trois chemins contrôlés," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14032 edited by Gubinelli, Massimiliano.
    • Handle: RePEc:dau:thesis:123456789/14032
    Note: dissertation
    as

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    File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/14032/2/2014PA090002.pdf
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    More about this item

    Keywords

    Chemin rugueux; Distribution contrôlé; Intégral de Young; Paraproduit; Chemin contrôlé; Rough path; Controlled distribution; Young intégration theory; Paraproduct; Controlled path;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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