### Abstract

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.

Original language | English |
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Pages (from-to) | 501-541 |

Number of pages | 41 |

Journal | Probability Theory and Related Fields |

Volume | 80 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1989 Feb 1 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Kawazu, K., Tamura, Y., & Tanaka, H. (1989). Limit theorems for one-dimensional diffusions and random walks in random environments.

*Probability Theory and Related Fields*,*80*(4), 501-541. https://doi.org/10.1007/BF00318905