### Abstract

Original language | English |
---|---|

Pages (from-to) | 389-416 |

Number of pages | 28 |

Journal | Stochastic Processes and their Applications |

Volume | 118 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2008 |

### Fingerprint

### Keywords

- random walk
- random environment
- logarithmic speeds
- almost sure behaviour
- slow transience

### Cite this

*Stochastic Processes and their Applications*,

*118*(3), 389-416. https://doi.org/10.1016/j.spa.2007.04.011

}

*Stochastic Processes and their Applications*, vol. 118, no. 3, pp. 389-416. https://doi.org/10.1016/j.spa.2007.04.011

**Logarithmic speeds for one-dimensional perturbed random walk in random environment.** / Menshikov, M. V.; Wade, Andrew R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Logarithmic speeds for one-dimensional perturbed random walk in random environment

AU - Menshikov, M. V.

AU - Wade, Andrew R.

PY - 2008/3

Y1 - 2008/3

N2 - We study the random walk in random environment on Z+ = f0; 1; 2; : : :g, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) random walk in random environment perturbed from Sinai's regime; (ii) simple random walk with random perturbation. We give almost sure results on how far the random walker is from the origin, for almost every environment. We give both upper and lower almost sure bounds. These bounds are of order (log t), for 2 (1;1), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution.

AB - We study the random walk in random environment on Z+ = f0; 1; 2; : : :g, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) random walk in random environment perturbed from Sinai's regime; (ii) simple random walk with random perturbation. We give almost sure results on how far the random walker is from the origin, for almost every environment. We give both upper and lower almost sure bounds. These bounds are of order (log t), for 2 (1;1), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution.

KW - random walk

KW - random environment

KW - logarithmic speeds

KW - almost sure behaviour

KW - slow transience

U2 - 10.1016/j.spa.2007.04.011

DO - 10.1016/j.spa.2007.04.011

M3 - Article

VL - 118

SP - 389

EP - 416

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 3

ER -