Averaging principle for diffusion processes via Dirichlet forms |
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Authors: | Florent Barret Max von Renesse |
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Institution: | 1. Max Planck Institut für Mathematik in den Naturwissenschaften, Inselstra?e 22, 04103, Leipzig, Germany 2. Universit?t Leipzig, Fakult?t für Mathematik und Informatik, Augustusplatz 10, 04109, Leipzig, Germany
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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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