  This paper studies, in dimensions greater than two, stationary diffusion
processes in random environment which are small, isotropic perturbations of
Brownian motion satisfying a finite range dependence. Such processes were first
considered in the continuous setting by Sznitman and Zeitouni [20]. Building
upon their work, it is shown by analyzing the associated elliptic
boundary-value problem that, almost surely, the smoothed (in the sense that the
boundary data is continuous) exit law of the diffusion from large domains
converges, as the domain's scale approaches infinity, to that of a Brownian
motion. Furthermore, a rate for the convergence is established in terms of the
modulus of the boundary condition.
