Komorowski, Tomasz; Olla, Stefano On homogenization of time-dependent random flows. (English) Zbl 0996.60040 Probab. Theory Relat. Fields 121, No. 1, 98-116 (2001). The authors consider the Itô stochastic differential equation \[ d{\mathbf x}(t;\omega,\sigma)={\mathbf V}(t,{\mathbf x}(t);\omega) dt +\sqrt{2} d{\mathbf w}(t),\quad {\mathbf x}(0)={\mathbf 0}, \] where \({\mathbf V}:{\mathbf R}\times{\mathbf R}^d\times\Omega\to{\mathbf R}^d\) is a zero mean, stationary, ergodic random vector field over a certain probability space \((\Omega,{\mathcal V},P)\). Assume that \({\mathbf V}\) is locally Lipschitz in \({\mathbf x}\) and \({\mathbf V}(t,{\mathbf x};\omega)=\nabla_{\mathbf x} \cdot{\mathbf H}(t,{\mathbf x};\omega)\), i.e., \({\mathbf V}\) is the divergence of some stationary anti-symmetric random field \({\mathbf H}(t,{\mathbf x};\omega).\) The authors prove that the laws of the trajectories \(\varepsilon {\mathbf x}(t/\varepsilon^2)\), \(t\geq 0,\) converge in probability with respect to \(\omega\), as \(\varepsilon\downarrow 0\), to the law of a Brownian motion with a nontrivial covariance matrix. Reviewer: Kestutis Kubilius (Vilnius) Cited in 1 ReviewCited in 15 Documents MSC: 60F17 Functional limit theorems; invariance principles 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 60G44 Martingales with continuous parameter Keywords:invariance principle; homogenization; martingale PDFBibTeX XMLCite \textit{T. Komorowski} and \textit{S. Olla}, Probab. Theory Relat. Fields 121, No. 1, 98--116 (2001; Zbl 0996.60040) Full Text: DOI