We provide exact computations for the drift of random walks in dependent random environments, including k-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron-Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment.
"A comparison of random walks in dependent random environments." Adv. in Appl. Probab. 48 (1) 199 - 214, March 2016.