Averaging principle for diffusion processes via Dirichlet forms

Florent Barret (1, 2, 3) , Max-K. von Renesse (2)

1 MPI-MiS - Max Planck Institute for Mathematics in the Sciences
2 Fakultät für Mathematik und Informatik
3 MODAL'X - Modélisation aléatoire de Paris X

We study diffusion processes driven by a Brownian motion with regular drift in a finite dimension setting. The drift has two components on different time scales, a fast conservative component and a slow dissipative component. Using the theory of Dirichlet form and Mosco-convergence we obtain simpler proofs, interpretations and new results of the averaging principle for such processes when we speed up the conservative component. As a result, one obtains an effective process with values in the space of connected level sets of the conserved quantities. The use of Dirichlet forms provides a simple and nice way to characterize this process and its properties.

Mots clés: stochastic diffusion processes; Averaging principle; Dirichlet forms; Mosco-convergence

Domaines: Probabilités [math.PR]

Florent Barret, Max-K. von Renesse. Averaging principle for diffusion processes via Dirichlet forms. Potential Analysis, 2014, 41 (4). ⟨hal-00844908v2⟩