Open Access
2009 The scaling limit of senile reinforced random walk.
Mark Holmes
Author Affiliations +
Electron. Commun. Probab. 14: 104-115 (2009). DOI: 10.1214/ECP.v14-1449


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.


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Mark Holmes. "The scaling limit of senile reinforced random walk.." Electron. Commun. Probab. 14 104 - 115, 2009.


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

zbMATH: 1187.60084
MathSciNet: MR2481670
Digital Object Identifier: 10.1214/ECP.v14-1449

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