Electronic Communications in Probability

The scaling limit of senile reinforced random walk.

Mark Holmes

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

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

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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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