Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

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

Menshikov, Mikhail V. and Wade, Andrew R. (2008) Logarithmic speeds for one-dimensional perturbed random walk in random environment. Stochastic Processes and their Applications, 118 (3). pp. 389-416. ISSN 0304-4149

[img]
Preview
PDF (strathprints013395.pdf)
strathprints013395.pdf

Download (322kB) | Preview

Abstract

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.