## 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