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MiS Preprint

Averaging via Dirichlet Forms

Florent Barret and Max von Renesse


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 mean to characterize this process and its properties.

MSC Codes:
60J45, 34C29, 70K70
Averaging principle, stochastic diffusion processes, Dirichlet forms, Mosco-convergence

Related publications

2014 Repository Open Access
Florent Barret and Max von Renesse

Averaging principle for diffusion processes via Dirichlet forms

In: Potential analysis, 41 (2014) 4, pp. 1033-1063