Limit theorems for one-dimensional diffusions and random walks in random environments |
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Authors: | Kiyoshi Kawazu Yozo Tamura Hiroshi Tanaka |
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Institution: | (1) Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi, Japan;(2) Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama, Japan |
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Abstract: | Summary 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. |
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