Persistent Random Walks. II. Functional Scaling Limits

@article{Cnac2018PersistentRW,
  title={Persistent Random Walks. II. Functional Scaling Limits},
  author={Peggy C{\'e}nac and Arnaud Le Ny and Basile de Loynes and Yoann Offret},
  journal={Journal of Theoretical Probability},
  year={2018},
  volume={32},
  pages={633-658}
}
We describe the scaling limits of the persistent random walks (PRWs) for which the recurrence has been characterized in Cénac et al. (J. Theor. Probab. 31(1):232–243, 2018). We highlight a phase transition phenomenon with respect to the memory: depending on the tails of the persistent time distributions, the limiting process is either Markovian or non-Markovian. In the memoryless situation, the limits are classical strictly stable Lévy processes of infinite variations, but the critical Cauchy… 
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