Oseledec's Multiplicative Ergodic Theorem is used to give recurrence and transience criteria for random walk in a random environment on the integers. These criteria generalize those given by Solomon in the nearest-neighbor case. The methodology for random environments is then applied to Markov chains with periodic transition functions to obtain recurrence and transience criteria for these processes as well.
Publié le : 1984-05-14
Classification:
Random walk in a random environment,
random walk in a periodic environment,
Markov chain,
transience,
recurrence,
Oseledec's Multiplicative Ergodic Theorem,
Lyapunov numbers,
linear equations with random coefficients,
60J10,
60J15
@article{1176993304,
author = {Key, Eric S.},
title = {Recurrence and Transience Criteria for Random Walk in a Random Environment},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 529-560},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993304}
}
Key, Eric S. Recurrence and Transience Criteria for Random Walk in a Random Environment. Ann. Probab., Tome 12 (1984) no. 4, pp. 529-560. http://gdmltest.u-ga.fr/item/1176993304/