A one-dimensional diffusion process in a Wiener medium (Q1085896)

The author studies a one-dimensional diffusion process in a random medium generated by a Wiener process. Via scale and time transformations and using the self-similarity of the medium process, the asymptotic behavior, the exit time from depression etc. of the diffusion process are investigated. The method used and the results obtained here are analogous to the case of a one-dimensional random walk in a random medium with independent increments as studied by \textit{Ya. G. Sinaj} [Teor. Veroyatn. Primen. 27, 247-258 (1982; Zbl 0497.60065); English translation in Theory Probab. Appl. 27, 256-268 (1982)].