Averaging principle for diffusion processes via Dirichlet forms

2013/07/16 by Florent Barret, Barret, Florent, Max‐K. von Renesse +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #stochastic dynamics and bifurcation

paper · doi:10.48550/arxiv.1307.4248

openalex publication_date 2013/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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