Recurrence of Multidimensional Persistent Random Walks. Fourier and Series Criteria

@article{Cnac2017RecurrenceOM,
  title={Recurrence of Multidimensional Persistent Random Walks. Fourier and Series Criteria},
  author={Peggy C{\'e}nac and Basile de Loynes and Yoann Offret and Arnaud Rousselle},
  journal={arXiv: Probability},
  year={2017}
}
  • Peggy Cénac, Basile de Loynes, +1 author Arnaud Rousselle
  • Published 2017
  • Mathematics
  • arXiv: Probability
  • The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal Markov chain: they admit Markov random walk skeletons. A recurrence versus transience dichotomy is highlighted. We first give a sufficient Fourier criterion for the recurrence, close to the usual Chung-Fuchs one, assuming in addition the positive recurrence of… CONTINUE READING

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