The Annals of Probability

Recurrence and Transience Criteria for Random Walk in a Random Environment

Eric S. Key

Full-text: Open access

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


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