Large deviations for diffusions: Donsker and Varadhan meet Freidlin and Wentzell
Résumé
We consider a diffusion process on R n and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the expectation of the Freidlin-Wentzell functional per unit of time. As an application of this result, we obtain a variational representation of the rate function for the Gallavotti-Cohen observable in the small noise and large time limits.
Mots clés
2010 Mathematics Subject Classification. Primary 60J60 60F10
Secondary 82C31 Large deviations Empirical process Γ-convergence Gallavotti-Cohen observable
2010 Mathematics Subject Classification. Primary 60J60
60F10
Secondary 82C31 Large deviations
Empirical process
Γ-convergence
Gallavotti-Cohen observable
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)