THE LOCAL TIME OF SIMPLE RANDOM-WALK IN RANDOM ENVIRONMENT

Two integral tests are established, which characterize respectively Le vy's upper and lower classes for the local time of Sinai's simple rand om walk in random environment. The weak convergence of the local time is also studied, and the limiting distribution determined. Our results can be applied to a class of diffusion processes with random potentia ls which asymptotically behave like Brownian motion.