Non-homogeneous random walks on a semi-infinite strip

@article{Georgiou2014NonhomogeneousRW,
  title={Non-homogeneous random walks on a semi-infinite strip},
  author={Nicholas Georgiou and Andrew R. Wade},
  journal={Stochastic Processes and their Applications},
  year={2014},
  volume={124},
  pages={3179-3205}
}
We study the asymptotic behaviour of Markov chains (Xn,ηn) on Z+×S, where Z+ is the non-negative integers and S is a finite set. Neither coordinate is assumed to be Markov. We assume a moments bound on the jumps of Xn, and that, roughly speaking, ηn is close to being Markov when Xn is large. This departure from much of the literature, which assumes that ηn is itself a Markov chain, enables us to probe precisely the recurrence phase transitions by assuming asymptotically zero drift for Xn given… Expand
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