Logarithmic speeds for onedimensional perturbed random walk in random environment
Menshikov, Mikhail V. and Wade, Andrew R. (2008) Logarithmic speeds for onedimensional perturbed random walk in random environment. Stochastic Processes and their Applications, 118 (3). pp. 389416. ISSN 03044149

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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.
Item type:  Article 

ID code:  13395 
Keywords:  random walk, random environment, logarithmic speeds, almost sure behaviour, slow transience, Probabilities. Mathematical statistics, Mathematics, Modelling and Simulation, Applied Mathematics, Statistics and Probability 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  12 Nov 2009 13:50 
Last modified:  29 Apr 2016 15:20 
URI:  http://strathprints.strath.ac.uk/id/eprint/13395 