Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 20 (2015), paper no. 67, 10 pp.
Strong transience of one-dimensional random walk in a random environment
A transient stochastic process is considered strongly transient if conditioned on returning to the starting location, the expected time it takes to return the the starting location is finite. We characterize strong transience for a one-dimensional random walk in a random environment. We show that under the quenched measure transience is equivalent to strong transience, while under the averaged measure strong transience is equivalent to ballisticity (transience with non zero limiting speed).
Electron. Commun. Probab., Volume 20 (2015), paper no. 67, 10 pp.
Accepted: 26 September 2015
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K37: Processes in random environments
Secondary: 60G50: Sums of independent random variables; random walks
This work is licensed under a Creative Commons Attribution 3.0 License.
Peterson, Jonathon. Strong transience of one-dimensional random walk in a random environment. Electron. Commun. Probab. 20 (2015), paper no. 67, 10 pp. doi:10.1214/ECP.v20-4352. https://projecteuclid.org/euclid.ecp/1465320994