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Slow recurrent regimes for a class of one-dimensional stochastic growth models

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  • Adam, Etienne

Abstract

We classify the possible behaviors of a class of one-dimensional stochastic recurrent growth models. In our main result, we obtain nearly optimal bounds for the tail of hitting times of some compact sets. If the process is an aperiodic irreducible Markov chain, we determine whether it is null recurrent or positive recurrent and in the latter case, we obtain a subgeometric convergence of its transition kernel to its invariant measure. We apply our results in particular to state-dependent Galton–Watson processes and we give precise estimates of the tail of the extinction time.

Suggested Citation

  • Adam, Etienne, 2018. "Slow recurrent regimes for a class of one-dimensional stochastic growth models," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2905-2922.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:2905-2922
    DOI: 10.1016/j.spa.2017.10.005
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    References listed on IDEAS

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    1. Aspandiiarov, S. & Iasnogorodski, R., 1997. "Tails of passage-times and an application to stochastic processes with boundary reflection in wedges," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 115-145, February.
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