Zero White Noise Limit through Dirichlet forms,with application to diffusions in a random medium

Summary We study the Zero White Noise Limit for diffusions in a continuous multidimensional medium: given a continuous function on ⁿ ,W, we consider diffusions whose drift term is the gradient ofW and whose diffusion coefficient is constant equal to . We describe the asymptotics of the exit time from a domain and of the law of the process when tends to zero. By applying these results to a random self-similar mediumW we prove limit theorems for a diffusion in a random medium. Our theorems agree with results usually proved through the large deviation principle, although, in our setup, this last tool is not available. We extend to the multidimensional case properties of diffusions in a random medium already known in one dimension.