The Annals of Probability
- Ann. Probab.
- Volume 12, Number 2 (1984), 529-560.
Recurrence and Transience Criteria for Random Walk in a Random Environment
Abstract
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.
Article information
Source
Ann. Probab., Volume 12, Number 2 (1984), 529-560.
Dates
First available in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993304
Digital Object Identifier
doi:10.1214/aop/1176993304
Mathematical Reviews number (MathSciNet)
MR735852
Zentralblatt MATH identifier
0545.60066
JSTOR
links.jstor.org
Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J15
Keywords
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
Citation
Key, Eric S. Recurrence and Transience Criteria for Random Walk in a Random Environment. Ann. Probab. 12 (1984), no. 2, 529--560. doi:10.1214/aop/1176993304. https://projecteuclid.org/euclid.aop/1176993304
