Yozo Tamura

Limit theorems for one-dimensional diffusions and random walks in random environments

SummaryThe limiting behavior of one-dimensional diffusion process in an asymptotically self-similar random environment is investigated through the extension of Broxs 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.

Recurrence of the Brownian Motion in Multidimensional Semi-selfsimilar Environments and Gaussian Environments

Asymptotic behavior of the one-dimensional Brownian motion in general random environments has been investigated by many researchers. However, many of the methods used in the argument are available only for the one-dimensional case. In this paper the multi-dimensional case of the problem is considered, and we obtain some sufficient conditions for recurrence of the multi-dimensional Brownian motion in random environments. By using the sufficient conditions we show that the recurrence of the Brownian motion in Gaussian environments under some conditions on the correlation functions.