  We study behavior in space and time of random walks in an i.i.d. random
environment on Z^d, d>=3. It is assumed that the measure governing the
environment is isotropic and concentrated on environments that are small
perturbations of the fixed environment corresponding to simple random walk. We
develop a revised and extended version of the paper of Bolthausen and Zeitouni
(2007) on exit laws from large balls, which, as we hope, is easier to follow.
Further, we study mean sojourn times in balls.
  This work is part of the author's PhD thesis under the supervision of Erwin
Bolthausen. A generalization of the results on exit measures to certain
anisotropic random walks in random environment is available at arXiv:1309.3169.
