Moderate Deviations for Mean Field Particle Models

Pierre del Moral (1, 2, 3) , Shulan Hu (4) , Liming Wu (5)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 IMB - Institut de Mathématiques de Bordeaux
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 Department of Statistics
5 CAS - Chinese Academy of Sciences [Beijing]

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.

Mots clés: Moderate deviations; interacting particle systems; exponential inequalities; functional central limit theorems; convergence of empirical processes; large deviations for projective limits.; large deviations for projective limits

Domaines: Probabilités [math.PR]

Pierre del Moral, Shulan Hu, Liming Wu. Moderate Deviations for Mean Field Particle Models. [Research Report] 2012, pp.37. ⟨hal-00687827⟩