Electronic Communications in Probability

The scaling limit of senile reinforced random walk.

Mark Holmes

Full-text: Open access

Abstract

This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable conditions, when T has heavy tails the scaling limit is the so-called fractional kinetics process, a random time-change of Brownian motion. The proof uses the standard tools of time-change and invariance principles for additive functionals of Markov chains.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 10, 104-115.

Dates
Accepted: 19 February 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234719

Digital Object Identifier
doi:10.1214/ECP.v14-1449

Mathematical Reviews number (MathSciNet)
MR2481670

Zentralblatt MATH identifier
1187.60084

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Holmes, Mark. The scaling limit of senile reinforced random walk. Electron. Commun. Probab. 14 (2009), paper no. 10, 104--115. doi:10.1214/ECP.v14-1449. https://projecteuclid.org/euclid.ecp/1465234719


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