Environment viewed from the particle and slowdown for ballistic RWRE in low dimensions

We consider a random walk in a random environment on Zd under ballisticity condition (T). We show the existence of the invariant measure Q with respect to the environment viewed from the particle for d=2 and d=3, which disproves a conjecture made in [3] regarding the two-dimensional case. We also prove tail estimates for the Radon-Nikodym derivative dQ∕dP, where P is the original distribution on the environment. Lastly, we provide nearly sharp tail bounds for regeneration times for d=3.