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A martingale approach to homogenization of unbounded random flows. (English) Zbl 0902.60028

Summary: We study the asymptotic behavior of Brownian motion in steady, unbounded incompressible random flows. We prove an invariance principle for almost all realizations of random flows. The key compactness result is obtained by Moser’s iterative scheme in PDE theory.

MSC:

60F17 Functional limit theorems; invariance principles
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[24] DAVIS, CALIFORNIA 95616-8633 EAST LANSING, MICHIGAN 48824 E-MAIL: fannjian@math.ucdavis.edu E-MAIL: komorow@math.msu.edu
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