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.
"A martingale approach to homogenization of unbounded random flows." Ann. Probab. 25 (4) 1872 - 1894, October 1997. https://doi.org/10.1214/aop/1023481115