Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux

Type de document

NOTE INTERNE OU DE TRAVAIL

Langue

anglais

Auteur

LEGOLL ; LELIEVRE ; OLLA

Résumé / Abstract

Starting from the overdamped Langevin dynamics in R, we consider a scalar Markov process ¾t which approximates the dynamics of the first component X1t. In the previous work [F. Legoll, T. Lelievre, Nonlinearity 2010], the fact that (¾t)te0 is a good approximation of (X1t)te0 is proven in terms of time marginals, under assumptions quantifying the timescale separation between the first component and the other components of Xt. Here, we prove an upper bound on the trajectorial error E(sup0dtdT##X1t¾t##), for any T>0, under a similar set of assumptions. We also show that the technique of proof can be used to obtain quantitative averaging results.