Averaging via Dirichlet Forms

Florent Barret and Max von Renesse

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Submission date: 15. Jul. 2013
Pages: 29
published in: Potential analysis, 41 (2014) 4, p. 1033-1063 
DOI number (of the published article): 10.1007/s11118-014-9405-x
Bibtex
with the following different title: Averaging principle for diffusion processes via Dirichlet forms
MSC-Numbers: 60J45, 34C29, 70K70
Keywords and phrases: Averaging principle, stochastic diffusion processes, Dirichlet forms, Mosco-convergence
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Abstract:
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.