Averaging principle for diffusion processes via Dirichlet forms

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...

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Bibliographic Details
Main Authors Barret, Florent, Von Renesse, Max-K
Format Journal Article
LanguageEnglish
Published 16.07.2013
Subjects
Mathematics - Probability
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Summary: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.
DOI:10.48550/arxiv.1307.4248