### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

*Probability Theory and Related Fields*,

*80*(4), 501-541. https://doi.org/10.1007/BF00318905

**Limit theorems for one-dimensional diffusions and random walks in random environments.** / Kawazu, Kiyoshi; Tamura, Yozo; Tanaka, Hiroshi.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 80, no. 4, pp. 501-541. https://doi.org/10.1007/BF00318905

}

TY - JOUR

T1 - Limit theorems for one-dimensional diffusions and random walks in random environments

AU - Kawazu, Kiyoshi

AU - Tamura, Yozo

AU - Tanaka, Hiroshi

PY - 1989/2

Y1 - 1989/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001429917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001429917&partnerID=8YFLogxK

U2 - 10.1007/BF00318905

DO - 10.1007/BF00318905

M3 - Article

AN - SCOPUS:0001429917

VL - 80

SP - 501

EP - 541

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -