Asymptotic behavior of stochastic processes in random environments

We introduce investigations of random walks and diffusion processes in random environments. Such processes have two kinds of randomness. The long-time behavior of such processes has been studied by many mathematicians. In many cases, the ‘average speed’ of a stochastic process in a random environment is much slower than that of a stochastic process in a fixed environment. We introduce such results for various models. We also introduce results on recurrence and transience properties of such processes.