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hal-00687827, version 1

Moderate Deviations for Mean Field Particle Models

Pierre Del Moral (, http://www.math.u-bordeaux.fr/~delmoral/) 1, 2, 3, Shulan Hu () a, 4, Liming Wu () b, 5

(2012)

Résumé : This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of fi nite and bounded measures as well as for the corresponding stochastic processes on some class of functions equipped with the uniform topology. Our approach is based on an original semigroup analysis combined with stochastic perturbation techniques and projective limit large deviation methods.

  • a –  Zhongnan University of Economics and Law
  • b –  Institute of Applied Mathematics, Chinese Academy of Sciences
  • 1 :  ALEA (INRIA Bordeaux - Sud-Ouest)
  • INRIA – Université de Bordeaux – CNRS : UMR5251
  • 2 :  Institut de Mathématiques de Bordeaux (IMB)
  • CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
  • 3 :  Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
  • Polytechnique - X – CNRS : UMR7641
  • 4 :  Zhongnan University of Economics and Law
  • Zhongnan University of Economics and Law
  • 5 :  Chinese Academy of Sciences
  • Institute of Applied Mathematics, Chinese Academy of Sciences
  • Domaine : Mathématiques/Probabilités
  • Mots-clés : Moderate deviations – interacting particle systems – exponential inequalities – functional central limit theorems – convergence of empirical processes – large deviations for projective limits.
 
  • hal-00687827, version 1
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  • Contributeur : Pierre Del Moral <>
  • Soumis le : Dimanche 15 Avril 2012, 12:16:53
  • Dernière modification le : Dimanche 15 Avril 2012, 21:03:43