Diffusion in a singular random environment (Q914263)

Using Dirichlet forms, the author shows the existence of a class of one- dimensional diffusion processes whose drifts are the first derivatives (in the sense of Schwartz) of bounded upper-semicontinuous functions. The space of drifts is endowed with a translation-invariant and ergodic probability measure, producing a diffusion in a random environment. An invariance principle is then proven for the rescaled diffusion. The use of scale functions and speed measures instead of Dirichlet forms for the one-dimensional diffusions would have simplified the author's hypothesis and arguments.