Averaging principle for diffusion processes via Dirichlet forms

Florent Barret; Max-K. Von Renesse

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arXiv · 1307.4248

Averaging principle for diffusion processes via Dirichlet forms

Florent Barret·Max-K. Von Renesse

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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 way to characterize this process and its properties.

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Florent Barret, Max-K. Von Renesse. 2014-03-26. Averaging principle for diffusion processes via Dirichlet forms. https://arxiv.org/abs/1307.4248

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