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.
"The scaling limit of senile reinforced random walk.." Electron. Commun. Probab. 14 104 - 115, 2009. https://doi.org/10.1214/ECP.v14-1449