Electronic Communications in Probability

Strong transience of one-dimensional random walk in a random environment

Jonathon Peterson

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Abstract

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). 

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 67, 10 pp.

Dates
Accepted: 26 September 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320994

Digital Object Identifier
doi:10.1214/ECP.v20-4352

Mathematical Reviews number (MathSciNet)
MR3407211

Zentralblatt MATH identifier
1328.60229

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60G50: Sums of independent random variables; random walks

Keywords
random walk in random environment strong transience

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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