Markov chains with heavy-tailed increments and asymptotically zero drift

  title={Markov chains with heavy-tailed increments and asymptotically zero drift},
  author={Nicholas Georgiou and Mikhail Menshikov and Dimitri Petritis and Andrew R. Wade},
  journal={Electronic Journal of Probability},
We study the recurrence/transience phase transition for Markov chains on $\mathbb{R}_+$, $\mathbb{R}$, and $\mathbb{R}^2$ whose increments have heavy tails with exponent in $(1,2)$ and asymptotically zero mean. This is the infinite-variance analogue of the classical Lamperti problem. On $\mathbb{R}_+$, for example, we show that if the tail of the positive increments is about $c y^{-\alpha}$ for an exponent $\alpha \in (1,2)$ and if the drift at $x$ is about $b x^{-\gamma}$, then the critical… Expand
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