A class of diffusions on the line is considered whose drifts are generalized functions (Schwartzian distributions). A probability measure is put on this space of drifts, giving a diffusion in a random environment. An invariance principle is then proven for the rescaled diffusion, generalizing a result of De Masi, Ferrari, Goldstein and the author.
Ann. Probab.
18(1):
50-67
(January, 1990).
DOI: 10.1214/aop/1176990937