In this work we prove the equivalence between static and dynamic points of views for certain ballistic random walks in random environment on Zd, when d greater than or equal to 4 and the disorder is low. Our techniques also enable us to derive in the same setting a functional central limit theorem for almost every realization of the environment. We also provide an example where the equivalence between static and dynamic points of views breaks down.
"Turbulence Without Pressure: Existence of the Invariant Measure." Methods Appl. Anal. 9 (3) 463 - 468, September 2002.