The limiting behavior of one-dimensional diffusion process in an asymptotically self-similar random environment is investigated through the extension of Brox's method. Similar problems are then discussed for a random walk in a random environment with the aid of optional sampling from a diffusion model; an extension of the result of Sinai is given in the case of asymptotically self-similar random environments.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty