We study two typical examples of countable Markov chains in random
environment using the Lyapunov functions method: random walk and random string
in random environment. In each case we construct an explicit Lyapunov function.
Investigating the behavior of this function, we get the classification for
recurrence, transience, ergodicity. We obtain new results for random strings in
random environment, though we simply review well-known results for random walks
using our approach.
Publié le : 1998-10-14
Classification:
Random walk,
random string,
Lyapunov function,
random medium,
disordered systems,
product of random matrices,
Lyapunov exponents,
60J10,
60J80
@article{1022855869,
author = {Comets, Francis and Menshikov, Mikhail and Popov, Serguei},
title = {Lyapunov functions for random walks and strings in random
environment},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1433-1445},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855869}
}
Comets, Francis; Menshikov, Mikhail; Popov, Serguei. Lyapunov functions for random walks and strings in random
environment. Ann. Probab., Tome 26 (1998) no. 1, pp. 1433-1445. http://gdmltest.u-ga.fr/item/1022855869/